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.

Paper's Title:

Inclusion and Neighborhood Properties for Certain Subclasses of Analytic Functions Associated with Convolution Structure

Author(s):

M. K. Aouf

Mathematics Department,
Faculty of Science,
Mansoura University 35516,
Egypt.
mkaouf127@yahoo.com

Abstract:

In this paper we introduce and investigate two new subclasses of multivalently analytic functions of complex order defined by using the familiar convolution structure of analytic functions. In this paper we obtain the coefficient estimates and the consequent inclusion relationships involving the neighborhoods of the p-valently analytic functions.

Paper's Title:

On Convergence Theorems of an Implicit Iterative Process with Errors for a Finite Family of Asymptotically quasi I-nonexpansive Mappings

Author(s):

Farrukh Mukhamedov and Mansoor Saburov

Department of Computational & Theoretical Sciences,
Faculty of Sciences, International Islamic University Malaysia,
P.O. Box, 141, 25710, Kuantan,
Malaysia

farrukh_m@iiu.edu.my

msaburov@gmail.com

http://www.iium.edu.my

Abstract:

In this paper we prove the weak and strong convergence of the implicit iterative process with errors to a common fixed point of a finite family {T_j}^N_i=1 of asymptotically quasi I_j-nonexpansive mappings as well as a family of {Ij}^N_j=1 of asymptotically quasi nonexpansive mappings in the framework of Banach spaces. The obtained results improve and generalize the corresponding results in the existing literature.

Paper's Title:

On Reformations of 2--Hilbert Spaces

Author(s):

M. Eshaghi Gordji, A. Divandari, M. R. Safi and Y. J. Cho

Department of Mathematics, Semnan University,
P.O. Box 35195--363, Semnan,
Iran

meshaghi@semnan.ac.ir, madjid.eshaghi@gmail.com

Department of Mathematics, Semnan University,
Iran

Divandari@sun.Semnan.ac.ir

Department of Mathematics, Semnan University,
Iran

safi@semnan.ac.ir, SafiMohammadReza@yahoo.com

Department of Mathematics Education and the RINS,
Gyeongsang National University
Chinju 660-701,
Korea

yjcho@gnu.ac.kr

Abstract:

In this paper, first, we introduce the new concept of (complex) 2--Hilbert spaces, that is, we define the concept of 2--inner product spaces with a complex valued 2--inner product by using the 2--norm. Next, we prove some theorems on Schwartz's inequality, the polarization identity, the parallelogram laws and related important properties. Finally, we give some open problems related to 2--Hilbert spaces.

Paper's Title:

A Comparison Between Two Different Stochastic Epidemic Models with Respect to the Entropy

Author(s):

Farzad Fatehi and Tayebe Waezizadeh

Department of Mathematics,
University of Sussex,
Brighton BN1 9QH,
UK.
E-mail: f.fatehi@sussex.ac.uk
URL: http://www.sussex.ac.uk/profiles/361251

Department of Pure Mathematics, Faculty of Mathematics and Computer,
Shahid Bahonar University of Kerman,
Kerman 76169-14111,
Iran.
E-mail: waezizadeh@uk.ac.ir
URL: http://academicstaff.uk.ac.ir/en/tavaezizadeh

Abstract:

In this paper at first a brief history of mathematical models is presented with the aim to clarify the reliability of stochastic models over deterministic models. Next, the necessary background about random variables and stochastic processes, especially Markov chains and the entropy are introduced. After that, entropy of SIR stochastic models is computed and it is proven that an epidemic will disappear after a long time. Entropy of a stochastic mathematical model determines the average uncertainty about the outcome of that random experiment. At the end, we introduce a chain binomial epidemic model and compute its entropy, which is then compared with the DTMC SIR epidemic model to show which one is nearer to reality.

Paper's Title:

A Self-adaptive Subgradient Extragradient Algorithm for Variational Inequality Problems and Fixed Point Problems in Banach Spaces

Author(s):

F. U. Ogbuisi

School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.

Department of Mathematics,
University of Nigeria, Nsukka,
Nigeria.
E-mail: ferdinard.ogbuisi@unn.edu.ng fudochukwu@yahoo.com

Abstract:

In this paper, we propose and analyze a type of subgradient extragradient algorithm for the approximation of a solution of variational inequality problem which is also a common fixed point of an infinite family of relatively nonexpansive mappings in 2-uniformly convex Banach spaces which are uniformly smooth. By using the generalized projection operator, we prove a strong convergence theorem which does not require the prior knowledge of the Lipschitz constant of cost operator. We further applied our result to constrained convex minimization problem, convex feasibility problem and infinite family of equilibrium problems. Our results improve and complement related results in 2-uniformly convex and uniformly smooth Banach spaces and Hilbert spaces.

Paper's Title:

Coexisting Attractors and Bubbling Route to Chaos in Modified Coupled Duffing Oscillators

Author(s):

B. Deruni¹, A. S. Hacinliyan^1,2, E. Kandiran³, A. C. Keles², S. Kaouache⁴, M.-S. Abdelouahab⁴, N.-E. Hamri⁴

¹Department of Physics,
University of Yeditepe,
Turkey.

²Department of Information Systems and Technologies,
University of Yeditepe,
Turkey

³Department of Software Development,
University of Yeditepe,
Turkey.

⁴Laboratory of Mathematics and their interactions,
University Center of Abdelhafid Boussouf,
Mila 43000,
Algeria.

E-mail: berc890@gmail.com
ahacinliyan@yeditepe.edu.tr
engin.kandiran@yeditepe.edu.tr
cihan.keles@yeditepe.edu.tr
s.kaouache@centr-univ-mila.dz
medsalah3@yahoo.fr
n.hamri@centre-univ-mila.dz

Abstract:

In this article dynamical behavior of coupled Duffing oscillators is analyzed under a small modification. The oscillators have cubic damping instead of linear one. Although single duffing oscillator has complex dynamics, coupled duffing systems possess a much more complex structure. The dynamical behavior of the system is investigated both numerically and analytically. Numerical results indicate that the system has double scroll attractor with suitable parameter values. On the other hand, bifurcation diagrams illustrate rich behavior of the system, and it is seen that, system enters into chaos with different routes. Beside classical bifurcations, bubbling route to chaos is observed for suitable parameter settings. On the other hand, Multistability of the system is indicated with the coexisting attractors, such that under same parameter setting the system shows different periodic and chaotic attractors. Moreover, chaotic synchronization of coupled oscillators is illustrated in final section.

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.

Paper's Title:

Nonlinear System of Mixed Ordered Variational Inclusions Involving XOR Operation

Author(s):

Iqbal Ahmad, Abdullah and Syed Shakaib Irfan

Department of Mechanical Engineering,
College of Engineering, Qassim University
Buraidah 51452, Al-Qassim,
Saudi Arabia.
E-mail: iqbal@qec.edu.sa, i.ahmad@qu.edu.sa

Zakir Husain Delhi College,
University of Delhi,
JLN Marg, New Delhi- 110 002,
India.
E-mail: abdullahdu@qec.edu.sa

Department of Mathematics,
Aligarh Muslim University, Aligarh,
India.
E-mail: shakaibirfan@gmail.com

Abstract:

In this work, we introduce and solve an NSMOVI frameworks system involving XOR operation with the help of a proposed iterative algorithm in real ordered positive Hilbert spaces. We discuss the existence of a solution of a considered system of inclusions involving XOR operation by applying the resolvent operator technique with XOR operation and also study the strong convergence of the sequences generated by the considered algorithm. Further, we give a numerical example in support of our considered problem which gives the grantee that all the proposed conditions of our main result are fulfilled.

Paper's Title:

Preserver of Local Spectrum of Skew-product Operators

Author(s):

Rohollah Parvinianzadeh^1,*, Meysam Asadipour² and Jumakhan Pazhman³

¹Department of Mathematics,
College of Sciences,
University of Yasouj,
Yasouj, 75918-74934,
Iran.
E-mail: r.parvinian@yu.ac.ir

²Department of Mathematics,
College of Sciences,
University of Yasouj,
Yasouj, 75918-74934,
Iran.
E-mail: Asadipour@yu.ac.ir

³Department of Mathematics,
Ghor Institute of higher education,
Afghanistan.
E-mail: jumapazhman@gmail.com

Abstract:

Let H and K be infinite-dimensional complex Hilbert spaces, and B(H) (resp. B(K)) be the algebra of all bounded linear operators on H (resp. on K). For an operator T∈ B(H) and a vector h∈ H, let σ_T(h) denote the local spectrum of T at h. For two nonzero vectors h₀∈ H and k₀∈ K, we show that if two maps φ₁ and φ₂ from B(H) into B(K) satisfy

σ_{φ1(T)φ2(S)*}(k₀)= σ_TS*(h₀})

for all T, S ∈ B(H), and their range containing all operators of rank at most two, then there exist bijective linear maps P : H→ K and Q : K→ H such that φ₁(T) = PTQ and φ₂(T)^* =Q^-1T^*P^-1 for all T ∈ B(H). Also, we obtain some interesting results in this direction.

Paper's Title:

On Statistically Φ-Convergence

Author(s):

Supama

Department of Mathematics,
Gadjah Mada University,
Yogyakarta 55281,
Indonesia.
E-mail: supama@ugm.ac.id

Abstract:

The idea of statistical convergence was introduced by Antoni Zygmund in 1935. Based on in the idea of Zygmund, Henry Fast and Hugo Steinhaus independently introduced a concept of statistical convergence as a generalization of an ordinary convergence in the same year 1951. In this paper, by using the Orlicz function, we introduce a concept of statistical Φ-convergence, as a generalization of the statistical convergence. Further, we observe some basic properties and some topological properties of the statistical Φ-convergent sequences

Paper's Title:

SQIRV Model for Omicron Variant with Time Delay

Author(s):

S. Dickson, S. Padmasekaran, G. E. Chatzarakis and S. L. Panetsos

Mathematics, Periyar University, Periyar Palkalai Nagar, Salem,
636011, Tamilnadu,
India.
E-mail: dickson@periyaruniversity.ac.in, padmasekarans@periyaruniversity.ac.in

Electrical and Electronic Engineering Educators, School of
Pedagogical and Technological Education (ASPETE),
Marousi 15122, Athens,
Greece.
E-mail: geaxatz@otenet.gr, spanetsos@aspete.gr

Abstract:

In order to examine the dynamics of the Omicron variant, this paper uses mathematical modelling and analysis of a SQIRV model, taking into account the delay in the conversion of susceptible individuals into infected individuals and infected individuals into recovered individuals. The pandemic was eventually controlled as a result of the massive delays. To assure the safety of the host population, this concept incorporates quarantine and the COVID-19 vaccine. Both local and global stability of the model are examined. It is found that the fundamental reproduction number affects both local and global stability conditions. Our findings show that asymptomatic cases caused by an affected population play an important role in increasing Omicron infection in the general population. The most recent data on the pandemic Omicron variant from Tamil Nadu, India, is verified.

Paper's Title:

On Some Nonlinear Retarded Integrodifferential Inequalities in Two and n Independent Variables and their Applications

Author(s):

Bitat Dalila and Khellaf Hassane

Department of Mathematics, Laboratory of Applied Mathematics and Modeling,
University of Constantine,
PO Box 325, Ain El Bey Road, Constantine 25017,
Algeria.
E-mail: bitat.dalila@umc.edu.dz khellafhassane@umc.edu.dz
URL: https://www.umc.edu.dz

Abstract:

In this paper, we establish some new nonlinear retarded integrodifferential inequalities in two and n independent variables. Some applications are given as illustration.

Paper's Title:

Higher Order Accurate Compact Schemes for Time Dependent Linear and Nonlinear Convection-Diffusion Equations

Author(s):

S. Thomas, Gopika P.B. and S. K. Nadupuri

Department of Mathematics
National Institute of Technology Calicut
Kerala
673601
India.
E-mail: sobinputhiyaveettil@gmail.com pbgopika@gmail.com nsk@nitc.ac.in
 

Abstract:

The primary objective of this work is to study higher order compact finite difference schemes for finding the numerical solution of convection-diffusion equations which are widely used in engineering applications. The first part of this work is concerned with a higher order exponential scheme for solving unsteady one dimensional linear convection-diffusion equation. The scheme is set up with a fourth order compact exponential discretization for space and cubic $C^1$-spline collocation method for time. The scheme achieves fourth order accuracy in both temporal and spatial variables and is proved to be unconditionally stable. The second part explores the utility of a sixth order compact finite difference scheme in space and Huta's improved sixth order Runge-Kutta scheme in time combined to find the numerical solution of one dimensional nonlinear convection-diffusion equations. Numerical experiments are carried out with Burgers' equation to demonstrate the accuracy of the new scheme which is sixth order in both space and time. Also a sixth order in space predictor-corrector method is proposed. A comparative study is performed of the proposed schemes with existing predictor-corrector method. The investigation of computational order of convergence is presented.

Paper's Title:

A General Fractional Control Scheme for Compound Combination Synchronization Between Different Fractional-Order Identical Chaotic Systems

Author(s):

Soumia Bensimessaoud and Smail Kaouache

Laboratory of Mathematics and their interactions, Abdelhafid Boussouf University Center, Mila, Algeria.
E-mail: soumiabensimessaoud@gmail.com, smailkaouache@gmail.com

Abstract:

In this paper, we aim to investigate the problem of compound combination synchronization (CCS) between four different fractional-order identical chaotic systems. Based on Laplace transformation and stability theory of linear dynamical systems, a new control law is proposed to assure the achievement of this kind of synchronization. Secondly, this control scheme is applied to realised CCS between four identical unified chaotic systems. Recall, that the proposed control scheme can be applied to wide classes of chaotic and hyperchaotic systems. Numerical simulations are given to show the effectiveness of the proposed method.

Paper's Title:

On Automorphisms and Bi-derivations of Semiprime Rings

Author(s):

Abu Zaid Ansari, Faiza Shujat, Ahlam Fallatah

Department of Mathematics,
Faculty of Science,
Islamic University of Madinah, Madinah
K.S.A.
E-mail: ansari.abuzaid@gmail.com, ansari.abuzaid@iu.edu.sa

Department of Mathematics
Faculty of Science
Taibah University, Madinah,
K.S.A.
E-mail: faiza.shujat@gmail.com, fullahkhan@taibahu.edu.sa

Department of Mathematics
Faculty of Science
Taibah University, Madinah,
K.S.A.
E-mail: Afallatah@taibahu.edu.sa
 

Abstract:

In this article, our goal is to figure out a functional equation involving automorphisms and bi-derivations on certain semiprime ring. Also, we characterize the structure of automorphism, in case of prime rings.

Paper's Title:

A New Iterative Approximation of a Split Fixed Point Constraint Equilibrium Problem

Author(s):

Musa Adewale Olona¹, Adhir Maharaj² and Ojen Kumar Narain³

¹School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: 219095783@stu.ukzn.ac.za

²Department of Mathematics,
Durban University of Technology, Durban,
South Africa.
E-mail: adhirm@dut.ac.za

³School 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 introduce an iterative algorithm for approximating an element in the solution set of the common split feasibility problem for fixed points of demimetric mappings and equilibrium problem for monotone mapping in real Hilbert spaces. Motivated by self-adaptive step size method, we incorporate the inertial technique to accelerate the convergence of the proposed method and establish a strong convergence of the sequence generated by the proposed algorithm. Finally, we present a numerical example to illustrate the significant performance of our method. Our results extend and improve some existing results in the literature.

Paper's Title:

Solving Fixed Point Problems and Variational Inclusions Using Viscosity Approximations

Author(s):

P. Patel, R. Shukla

Department of Mathematics, School of Advanced Sciences, VIT-AP University\\
Amaravati, 522237, Andhra Pradesh,
India.
E-mail: prashant.patel9999@gmail.com, prashant.p@vitap.ac.in

Department of Mathematical Sciences & Computing, Walter Sisulu University,
Mthatha 5117,
South Africa.
E-mail: rshukla@wsu.ac.za

Abstract:

This paper proposes a new algorithm to find a common element of the fixed point set of a finite family of demimetric mappings and the set of solutions of a general split variational inclusion problem in Hilbert spaces. The algorithm is based on the viscosity approximation method, which is a powerful tool for solving fixed point problems and variational inclusion problems. Under some conditions, we prove that the sequence generated by the algorithm converges strongly to this common solution.

Paper's Title:

New Fast Extragradient-like Methods for Non-Lipschitzian Pseudo-monotone Variational Inequalities

Author(s):

Morad Ali Peyvand

Department of Mathematics
Yasouj University
Yasouj,
Iran.
E-mail: peyvand@yu.ac.ir

Abstract:

An efficient double-projection method, with a new search strategy, is designed for solving variational inequalities in real Hilbert spaces with pseudo-monotone cost operator. Our proposed method uses a computationally inexpensive simple line search procedure based on local information of the operator and very weak conditions of parameters to obtain larger step sizes. A description of the algorithm along with its weak convergence is provided without assuming Lipschitz continuity. Also, a modification to the proposed method is presented, wherein the second projection onto the closed and convex subset is replaced with the one onto a subgradient half space. Numerical experiments and comparisons with related methods demonstrate the reliability and benefits of the proposed schemes.

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