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8: Paper Source PDF document

Paper's Title:

Common Fixed Point Results for Banach Operator Pairs and Applications to Best Approximation

Author(s):

Hemant Kumar Nashine

Department of Mathematics,
Disha Institute of Management and Technology,
Satya Vihar, Vidhansabha - Chandrakhuri Marg (Baloda Bazar Road), Mandir Hasaud,
Raipur - 492101(Chhattisgarh), India.

hemantnashine@rediffmail.com
nashine_09@rediffmail.com
 

Abstract:

The common fixed point results for Banach operator pair with generalized nonexpansive mappings in q-normed space have been obtained in the present work. As application, some more general best approximation results have also been determined without the assumption of linearity or affinity of mappings. These results unify and generalize various existing known results with the aid of more general class of noncommuting mappings.



8: Paper Source PDF document

Paper's Title:

Ostrowski Type Inequalities for Lebesgue Integral: a Survey of Recent Results

Author(s):

Sever S. Dragomir1,2

1Mathematics, School of Engineering & Science
Victoria University, PO Box 14428
Melbourne City, MC 8001,
Australia
E-mail: sever.dragomir@vu.edu.au

 
2DST-NRF Centre of Excellence in the Mathematical and Statistical Sciences,
School of Computer Science & Applied Mathematics,
University of the Witwatersrand,
Private Bag 3, Johannesburg 2050,
South Africa
URL: http://rgmia.org/dragomir 

Abstract:

The main aim of this survey is to present recent results concerning Ostrowski type inequalities for the Lebesgue integral of various classes of complex and real-valued functions. The survey is intended for use by both researchers in various fields of Classical and Modern Analysis and Mathematical Inequalities and their Applications, domains which have grown exponentially in the last decade, as well as by postgraduate students and scientists applying inequalities in their specific areas.



6: Paper Source PDF document

Paper's Title:

Some Convergence Results for  Jungck-Am Iterative Process In Hyperbolic Spaces

Author(s):

Akindele Adebayo Mebawondu and Oluwatosin Temitope Mewomo

School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: 216028272@stu.ukzn.ac.za, mewomoo@ukzn.ac.za

Abstract:

In this paper, we introduce a new three steps iterative process called Jungck-AM iterative process and show that the proposed iterative process can be used to approximate fixed points of Jungck-contractive type mappings and Jungck-Suzuki type mappings. In addition, we establish some strong and Δ-convergence results for the approximation of fixed points of Jungck-Suzuki type mappings in the frame work of uniformly convex hyperbolic space. Furthermore, we show that the newly proposed iterative process has a better rate of convergence compare to the Jungck-Noor, Jungck-SP, Jungck-CR and some existing iterative processes in the literature. Finally, stability, data dependency results for Jungck-AM iterative process is established and we present an analytical proof and numerical examples to validate our claim.



5: Paper Source PDF document

Paper's Title:

D-Iterative Method for Solving a Delay Differential Equation and a Two-Point Second-Order Boundary Value Problems in Banach Spaces

Author(s):

Francis Akutsah1, Akindele Adebayo Mebawondu2, Oluwatosin Babasola3, Paranjothi Pillay4 and Ojen Kumar Narain5

1School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: 216040405@stu.ukzn.ac.za, akutsah@gmail.com

2School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa. 
DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
Mountain Top University,
Prayer City, Ogun State,
Nigeria.
E-mail: dele@aims.ac.za

3Department of Mathematical Sciences,
University of Bath,
Claverton Down,
Bath, BA2 7AY
UK.
E-mail: ob377@bath.ac.uk

4School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: pillaypi@ukzn.ac.za

5School of Mathematics,
Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: naraino@ukzn.ac.za

Abstract:

The purpose of this paper is to re-establish the convergence, stability and data dependence results established by [2] and [3] by removing the strong assumptions imposed on the sequences which were used to obtain their results. In addition, we introduced a modified approach using the D-iterative method to solve a two-point second-order boundary value problem, and also obtain the solution of a delay differential equations using the obtained results in this paper. The results presented in this paper do not only extend and improve the results obtained in [2, 3], it further extends and improve some existing results in the literature.



3: Paper Source PDF document

Paper's Title:

New Implicit Kirk-Type Schemes for General Class of Quasi-Contractive Operators in Generalized Convex Metric Spaces

Author(s):

K. Rauf, O. T. Wahab and A. Ali

Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria.
E-mail: krauf@unilorin.edu.ng

Department of Statistics and Mathematical Sciences,
Kwara State University, Malete,
Nigeria.

Department of Mathematics,
Mirpur University of Science and Technology, Mirpur,
Pakistan.

Abstract:

In this paper, we introduce some new implicit Kirk-type iterative schemes in generalized convex metric spaces in order to approximate fixed points for general class of quasi-contractive type operators. The strong convergence, T-stability, equivalency, data dependence and convergence rate of these results were explored. The iterative schemes are faster and better, in term of speed of convergence, than their corresponding results in the literature. These results also improve and generalize several existing iterative schemes in the literature and they provide analogues of the corresponding results of other spaces, namely: normed spaces, CAT(0) spaces and so on.



3: Paper Source PDF document

Paper's Title:

Existence of Solution of Differential and Riemann-Liouville Equation Via Fixed Point Approach in Complex Valued b-Metric Spaces

Author(s):

K. Afassinou, A. A. Mebawondu, H. A. Abass and O. K. Narain

Department of Science Access,
University of Zululand, KwaDlangezwa,
South Africa.
E-mail: komia@aims.ac.za

DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
E-mail: dele@aims.ac.za

DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS),
Johannesburg,
South Africa.
E-mail: hammedabass548@gmail.com

School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: naraino@ukzn.ac.za

Abstract:

In this paper, we establish some fixed point and common fixed point results for a new type of generalized contractive mapping using the notion of C-class function in the framework of complex valued b-metric spaces. As an application, we establish the existence and uniqueness of a solution for Riemann-Liouville integral and ordinary differential equation in the framework of a complete complex valued b-metric spaces. The obtained results generalize and improve some fixed point results in the literature.



2: Paper Source PDF document

Paper's Title:

Robust Error Analysis of Solutions to Nonlinear Volterra Integral Equation in Lp Spaces

Author(s):

Hamid Baghani, Javad Farokhi-Ostad and Omid Baghani

Department of Mathematics, Faculty of Mathematics,
University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan,
Iran.
E-mail: h.baghani@gmail.com

Department of Mathematics, Faculty of Basic Sciences,
Birjand University of Technology, Birjand,
Iran.
E-mail: j.farrokhi@birjandut.ac.ir

Department of Mathematics and Computer Sciences,
Hakim Sabzevari University, P.O. Box 397, Sabzevar,
Iran.
E-mail: o.baghani@gmail.com

Abstract:

In this paper, we propose a novel strategy for proving an important inequality for a contraction integral equations. The obtained inequality allows us to express our iterative algorithm using a "for loop" rather than a "while loop". The main tool used in this paper is the fixed point theorem in the Lebesgue space. Also, a numerical example shows the efficiency and the accuracy of the proposed scheme.



2: Paper Source PDF document

Paper's Title:

Hermite-Hadamard Type Inequalities for k-Riemann Liouville Fractional Integrals Via Two Kinds of Convexity

Author(s):

R. Hussain1, A. Ali2, G. Gulshan3, A. Latif4 and K. Rauf5

1,2,3,4Department of Mathematics,
Mirpur University of Science and Technology, Mirpur.
Pakistan.
E-mail1rashida12@gmail.com
E-mail2: unigraz2009@yahoo.com
E-mail3: ghazalagulshan@yahoo.com
E-mail4: asialatif87@gmail.com

5Department of Mathematics,
University of Ilorin, Ilorin,
Nigeria.
E-mail5: krauf@unilorin.edu.ng

Abstract:

In this article, a fundamental integral identity including the first order derivative of a given function via k-Riemann-Liouville fractional integral is established. This is used to obtain further Hermite-Hadamard type inequalities involving left-sided and right-sided k-Riemann-Liouville fractional integrals for m-convex and (s,m)-convex functions respectively.



2: Paper Source PDF document

Paper's Title:

Kinematic Model for Magnetic Null-points in 2 Dimensions

Author(s):

Ali Khalaf Hussain Al-Hachami

Department of Mathematics,
College of Education For Pure Sciences,
Wasit University,
Iraq.
E-mail: alhachamia@uowasit.edu.iq

Abstract:

The adjacent configurations of two-dimensional magnetic null point centers are analyzed by an immediate examination about the null. The configurations are classified as either potential or non-potential. By then the non-potential cases are subdivided into three cases depending upon whether the component of current is less than, equal to or greater than a threshold current. In addition the essential structure of reconnection in 2D is examined. It unfolds that the manner by which the magnetic flux is rebuilt. In this paper, we center on the ramifications of kinematic arrangements; that is, we fathom just Maxwell's conditions and a resistive Ohm's law.



2: Paper Source PDF document

Paper's Title:

Generalised Models for Torsional Spine Reconnection

Author(s):

Ali Khalaf Hussain Al-Hachami

Department of Mathematics,
College of Education For Pure Sciences,
Wasit University,
Iraq.
E-mail: alhachamia@uowasit.edu.iq

Abstract:

Three-dimensional (3D) null points are available in wealth in the solar corona, and the equivalent is probably going to be valid in other astrophysical situations. On-going outcomes from sun oriented perceptions and from reproductions propose that reconnection at such 3D nulls may assume a significant job in the coronal dynamics. The properties of the torsional spine method of magnetic reconnection at 3D nulls are researched. Kinematic model are created, which incorporate the term ηJ that is spatially localised around the null, stretching out along the spine of the null. The null point is to research the impact of shifting the level of asymmetry of the null point magnetic field on the subsequent reconnection process where past examinations constantly considered a non-nonexclusive radially symmetric null. Specifically we analyse the rate of reconnection of magnetic flux at the spine of null point. Logical arrangements are determined for the enduring kinematic equation, and contrasted and the after effects of torsional spine reconnection models when the current is restricted in which the Maxwell conditions are illuminated. The geometry of the current layers inside which torsional spine reconnection happen is autonomous on the symmetry of the magnetic field. Torsional spine reconnection happens in a thin cylinder around the spine, with circular cross-segment when the fan eigenvalues are extraordinary. The short axis of the circle being along the solid field bearing. Just as it was discovered that the fundamental structure of the method of attractive reconnection considered is unaffected by changing the magnetic field symmetry, that is, the plasma flow is discovered rotational around the spine of null point. The spatiotemporal pinnacle current, and the pinnacle reconnection rate achieved, are found not to rely upon the level of asymmetry.



2: Paper Source PDF document

Paper's Title:

Fractional Integral Inequalities of Hermite-Hadamard Type for P-convex and Quasi-Convex Stochastic Process

Author(s):

Oualid Rholam, Mohammed Barmaki and Driss Gretet

National School of Applied Sciences (ENSA),
University Ibn Tofail,
B.P 242 Kenitra 14000,
phone number : +212606257757,
Morocco.
E-mail: oualid.rholam@uit.ac.ma

 
Science Faculty Ben M'sik,
University Hassan II,
B.P 7955 Av Driss El Harti Sidi Othmane 20700,
phone number : +212 5 22 70 46 71 ,
Morocco.
E-mail:  mohammed.barmaki@uit.ac.ma

National School of Applied Sciences (ENSA),
University Ibn Tofail,
B.P 242 Kenitra 14000,
phone number : +212661403557,
Morocco.
E-mail: driss.gretete@uit.ac.ma 

 

Abstract:

In this paper we consider the class of P-convex and Quasi-convex stochastic processes on witch we apply a general class of generalized fractional integral operator in order to establish new integral inequalities of Hermite-Hadammard type. then we obtain some results for well known types of fractional integrals. Results obtained in this paper may be starting point as well as a useful source of inspiration for further research in convex analysis.



1: Paper Source PDF document

Paper's Title:

Fekete-Szegö Inequality for Certain Class of Analytic Functions

Author(s):

V. Ravichandran, Maslina Darus, M. Hussain Khan, and  K. G. Subramanian

School of Mathematical Sciences, Universiti Sains Malaysia,
11800 Usm, Penang, Malaysia

vravi@cs.usm.my

School of Mathematical Sciences, Faculty of Sciences and Technology,
Ukm, Banki 43600, Malaysia

maslina@pkrisc.cc.ukm.my

Department of Mathematics, Islamiah College,
V
aniambadi 635 751, India

Department of Mathematics, Madras Christian College, Tambaram,
Chennai- 600 059, India

kgsmani@vsnl.net

Abstract:

In this present investigation, the authors obtain Fekete-Szegö inequality for a certain class of analytic functions f(z) for which lies in a region starlike with respect to 1 and symmetric with respect to the real axis. Also certain application of our main result for a class of functions defined by Hadamard product (convolution) is given. As a special case of our result we obtain Fekete-Szegö inequality for a class of functions defined through fractional derivatives. Also we obtain Fekete-Szegö inequality for the inverse functions.



1: Paper Source PDF document

Paper's Title:

Differential Sandwich Theorems for Some Subclasses of Analytic Functions

Author(s):

T. N. Shanmugam, V. Ravichandran and S. Sivasubramanian

Department of Mathematics, College of Engineering,
Anna university, Chennai 600 025,
India
shan@annauniv.edu
URL: http://www.annauniv.edu/shan

School of Mathematical Sciences,
Universiti Sains Malaysia,
11800 USM Penang,
Malaysia
vravi@cs.usm.my
URL: http://cs.usm.my/~vravi

Department of Mathematics, Easwari Engineering college,
Ramapuram, Chennai 600 089,
India
sivasaisastha@rediffmail.com


Abstract:

Let and be univalent in with We give some applications of first order differential subordination and superordination to obtain sufficient conditions for normalized analytic function with to satisfy



1: Paper Source PDF document

Paper's Title:

On Sandwich Theorems for Certain Subclass of Analytic Functions Involving Dziok-Srivastava Operator

Author(s):

T. N. Shanmugam, M. P. Jeyarama and A. Singaravelu

Department of Mathematics
College of Engineering, Anna University
Chennai - 600 025,
India
drtns2001@yahoo.com

Department of Mathematics
Easwari Engineering College
Ramapuram, Chennai - 600089
Tamilnadu, India
jeyaraman-mp@yahoo.co.i

Department of Mathematics
Valliammai Engineering College
Chennai - 603203
Tamilnadu, India.
asing-59@yahoo.com


Abstract:

The purpose of this present paper is to derive some subordination and superordination results for certain normalized analytic functions in the open unit disk, acted upon by Dziok-Srivastava operator. Relevant connections of the results, which are presented in this paper, with various known results are also considered.



1: Paper Source PDF document

Paper's Title:

Solving Fractional Transport Equation via Walsh Function

Author(s):

A. Kadem

L. M. F. N., Mathematics Department,
 University of Setif,
Algeria
abdelouahak@yahoo.fr
 

Abstract:

In this paper we give a complete proof of A method for the solution of fractional transport equation in three-dimensional case by using Walsh function is presented. The main characteristic of this technique is that it reduces these problems to those of solving a system of algebraic equations, thus greatly simplifying the problem.



1: Paper Source PDF document

Paper's Title:

Mapped Chebyshev Spectral Methods for Solving Second Kind Integral Equations on the Real Line

Author(s):

Ahmed Guechi and Azedine Rahmoune

Department of Mathematics, University of Bordj Bou Arréridj,
El Anasser, 34030, BBA,
Algeria.
E-mail: a.guechi2017@gmail.com
E-mail: a.rahmoune@univ-bba.dz

Abstract:

In this paper we investigate the utility of mappings to solve numerically an important class of integral equations on the real line. The main idea is to map the infinite interval to a finite one and use Chebyshev spectral-collocation method to solve the mapped integral equation in the finite interval. Numerical examples are presented to illustrate the accuracy of the method.



1: Paper Source PDF document

Paper's Title:

Convergence Speed of Some Random Implicit-Kirk-type Iterations for Contractive-type Random Operators

Author(s):

H. Akewe, K.S. Eke

Department of Mathematics,
Covenant University, 
Canaanland, KM 10, Idiroko Road, P. M. B. 1023, Ota, Ogun State,
Nigeria.
E-mail: hudson.akewe@covenantuniversity.edu.ng, kanayo.eke@covenantuniversity.edu.ng

Abstract:

The main aim of this paper is to introduce a stochastic version of multistep type iterative scheme called a modified random implicit-Kirk multistep iterative scheme and prove strong convergence and stability results for a class of generalized contractive-type random operators. The rate of convergence of the random iterative schemes are also examined through an example. The results show that our new random implicit kirk multistep scheme perform better than other implicit iterative schemes in terms of convergence and thus have good potentials for further applications in equilibrium problems in computer science, physics and economics.



1: Paper Source PDF document

Paper's Title:

Some Inequalities of the Hermite-Hadamard Type for k-Fractional Conformable Integrals

Author(s):

C.-J. Huang, G. Rahman, K. S. Nisar, A. Ghaffar and F. Qi

Department of Mathematics, Ganzhou Teachers College,
Ganzhou 341000, Jiangxi,
China.
E-mail: hcj73jx@126.com , huangcj1973@qq.com

Department of Mathematics, Shaheed Benazir Bhutto University,
Sheringal, Upper Dir, Khyber Pakhtoonkhwa,
Pakistan.
E-mail: gauhar55uom@gmail.com

Department of Mathematics, College of Arts and Science at Wadi Aldawaser, 11991,
Prince Sattam Bin Abdulaziz University, Riyadh Region,
Kingdom of Saudi Arabia.
E-mail: n.sooppy@psau.edu.sa, ksnisar1@gmail.com

Department of Mathematical Science, Balochistan University of Information Technology,
Engineering and Management Sciences, Quetta,
Pakistan.
E-mail: abdulghaffar.jaffar@gmail.com

School of Mathematical Sciences, Tianjin Polytechnic University,
Tianjin 300387,
China; Institute of Mathematics,
Henan Polytechnic University, Jiaozuo 454010, Henan,
China.
E-mail: qifeng618@gmail.com, qifeng618@qq.com

 

Abstract:

In the paper, the authors deal with generalized k-fractional conformable integrals, establish some inequalities of the Hermite-Hadamard type for generalized k-fractional conformable integrals for convex functions, and generalize known inequalities of the Hermite-Hadamard type for conformable fractional integrals.



1: Paper Source PDF document

Paper's Title:

A new approach to the study of fixed point for simulation functions with application in G-metric spaces

Author(s):

Komi Afassinou and Ojen Kumar Narain

Department of Mathematical Sciences, University of Zululand,
KwaDlangezwa,
South Africa.
E-mail: komia@aims.ac.za

School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: naraino@ukzn.ac.za

Abstract:

The purpose of this work is to generalize the fixed point results of Kumar et al. [11] by introducing the concept of (α,β)-Z-contraction mapping, Suzuki generalized (α,β)-Z-contraction mapping, (α,β)-admissible mapping and triangular (α,β)-admissible mapping in the frame work of G-metric spaces. Fixed point theorems for these class of mappings are established in the frame work of a complete G-metric spaces and we establish a generalization of the fixed point result of Kumar et al. [11] and a host of others in the literature. Finally, we apply our fixed point result to solve an integral equation.



1: Paper Source PDF document

Paper's Title:

Fekete-Szegö Inequality for Sakaguchi Type of functions in Petal Shaped Domain

Author(s):

E. K. Nithiyanandham and B. Srutha Keerthi

Division of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai - 600 048,
India.
E-mail: nithiyankrish@gmail.com

Division of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai - 600 048,
India.
E-mail: keerthivitmaths@gmail.com

Abstract:

In this paper, we estimate coefficient bounds,|a_2|,|a_3| and |a_4|, Fekete-Szegö inequality and Toeplitz determinant T2(2) and T3(1) for functions belonging to the following class

 

the function being holomorphic, we expand using Taylor series and obtain several corollaries and consequences for the main result.



1: Paper Source PDF document

Paper's Title:

Toeplitz Determinant for Sakaguchi Type Functions Under Petal Shaped Domain

Author(s):

B. Nandhini and B. Srutha Keerthi

Division of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai - 600 048,
India.
E-mail: nandhinibaskar1996@gmail.com

Division of Mathematics, School of Advanced Sciences,
Vellore Institute of Technology Chennai Campus,
Chennai - 600 048,
India.
E-mail: keerthivitmaths@gmail.com

Abstract:

We introduce a new general subclass GPt,ρ of Sakaguchi kind function on a Petal shaped domain. We obtain coefficients bounds and upper bounds for the Fekete-Szegö functional over the class. From these functions we obtain the bounds of first four coefficients, and then we have derived the Toeplitz determinant T2(2) and T3(1) whose diagonal entries are the coefficients of functions.



1: Paper Source PDF document

Paper's Title:

Coefficient Bounds for Sakaguchi Kind of Functions Associated with Sine Function

Author(s):

Serap Bulut, H. Priya and B. Srutha Keerth

Kocaeli University,
Faculty of Aviation and Space Sciences,
Arslanbey Campus, 41285 Kartepe-Kocaeli,
Turkey.
E-mail: serap.bulut@kocaeli.edu.tr

 
Department of Mathematics,
School of Advanced Sciences,
VIT Chennai Campus, Chennai - 600 048,
India.
E-mail: priyaharikrishnan18@gmail.com, priya.h2020@vitstudent.ac.in

Department of Mathematics,
School of Advanced Sciences,
VIT Chennai Campus, Chennai - 600 048,
India.
E-mail: keerthivitmaths@gmail.com, sruthakeerthi.b@vit.ac.in

 

Abstract:

In this paper, we introduce a new general subclass of analytic functions with respect to symmetric points in the domain of sine function. We obtain sharp coefficient bounds and upper bounds for the Fekete-Szegö functional. Also we get sharp bounds for the logarithmic coefficients of functions belonging to this new class.


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