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10: Paper Source PDF document

Paper's Title:

Some Inequalities Concerning Derivative and Maximum Modulus of Polynomials

Author(s):

N. K. Govil, A. Liman and W. M. Shah

Department of Mathematics & Statistics, 
Auburn University, Auburn,
Alabama 36849-5310,
U.S.A

Department of Mathematics,
National Institute of Technology,
Srinagar, Kashmir,
India - 190006

Department of Mathematics,
Kashmir University,
Srinagar, Kashmir,
India - 190006

govilnk@auburn.edu
abliman22@yahoo.com
wmshah@rediffmail.com

 
 

Abstract:

In this paper, we prove some compact generalizations of some well-known Bernstein type inequalities concerning the maximum modulus of a polynomial and its derivative in terms of maximum modulus of a polynomial on the unit circle. Besides, an inequality for self-inversive polynomials has also been obtained, which in particular gives some known inequalities for this class of polynomials. All the inequalities obtained are sharp.



8: Paper Source PDF document

Paper's Title:

An Lp Inequality for `Self-Reciprocal' Polynomials. II

Author(s):

M. A. Qazi

Department of Mathematics,
Tuskegee University,
Tuskegee, Alabama 36088
U.S.A.

qazima@aol.com

 

Abstract:

The main result of this paper is a sharp integral mean inequality for the derivative of a `self-reciprocal' polynomial.



7: 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.



2: Paper Source PDF document

Paper's Title:

An Algorithm to Compute Gaussian-Type Quadrature Formulae
that Integrate Polynomials and Some Spline Functions Exactly

Author(s):

Allal Guessab

Laboratoire de Mathématiques Appliquées,
Université de Pau, 64000, Pau,
France.
allal.guessab@univ-pau.fr
URL: http://www.univ-pau.fr/~aguessab/

Abstract:

It is well-known that for sufficiently smooth integrands on an interval, numerical integration can be performed stably and efficiently via the classical (polynomial) Gauss quadrature formulae. However, for many other sets of integrands these quadrature formulae do not perform well. A very natural way of avoiding this problem is to include a wide class among arbitrary functions (not necessary polynomials) to be integrated exactly. The spline functions are natural candidates for such problems. In this paper, after studying Gaussian type quadrature formulae which are exact for spline functions and which contain boundary terms involving derivatives at both end points, we present a fast algorithm for computing their nodes and weights. It is also shown, taking advantage of the close connection with ordinary Gauss quadrature formula, that the latter are computed, via eigenvalues and eigenvectors of real symmetric tridiagonal matrices. Hence a new class of quadrature formulae can then be computed directly by standard software for ordinary Gauss quadrature formula. Comparative results with classical Gauss quadrature formulae are given to illustrate the numerical performance of the approach.



2: Paper Source PDF document

Paper's Title:

Asymptotic Inequalities for the Maximum Modulus of the Derivative of a Polynomial

Author(s):

Clément Frappier


Département de Mathématiques et de Génie industriel École Polytechnique de Montréal,
C.P.~6079, succ. Centre-ville Montréal (Québec),
H3C 3A7, CANADA


clement.frappier@polymtl.ca.

 

Abstract:

Let be an algebraic polynomial of degree ≤n, and let ∥p∥= max {|p(z)|:|z| = 1}. We study the asymptotic behavior of the best possible constant φn,k (R), for k = 0 and k=1, in the inequality ∥p'(Rz)∥ + φn,k (R) |ak| ≤ nRn-1p∥, R → ∞.



2: Paper Source PDF document

Paper's Title:

Existence Results for Second Order Impulsive Functional Differential Equations with Infinite Delay

Author(s):

M. Lakrib, A. Oumansour and K. Yadi  

Laboratoire de Mathématiques, Université Djillali
Liabées, B.P. 89 Sidi Bel Abbès 22000, Algérie
mlakrib@univ-sba.dz
oumansour@univ-sba.dz

Laboratoire de Mathématiques, Université Abou Bekr
Belkaid, B.P. 119 Tlemcen 13000, Algérie
k_yadi@mail.univ-tlemcen.dz

Abstract:

In this paper we study the existence of solutions for second order impulsive functional differential equations with infinite delay. To obtain our results, we apply fixed point methods.



2: Paper Source PDF document

Paper's Title:

On the Sendov Conjecture for a Root Close to the Unit Circle

Author(s):

Indraneel G. Kasmalkar

Department of Mathematics,
University of California,
Berkeley, CA 94720
United States of America

E-mail: indraneelk@berkeley.edu 

Abstract:

On Sendov's conjecture, T. Chijiwa quantifies the idea stated by V. Vâjâitu and A. Zaharescu (and M. J. Miller independently), namely that if a polynomial with all roots inside the closed unit disk has a root sufficiently close to the unit circle then there is a critical point at a distance of at most one from that root. Chijiwa provides an estimate of exponential order for the required 'closeness' of the root to the unit circle so that such a critical point may exist. In this paper, we will improve this estimate to polynomial order by making major modifications and strengthening inequalities in Chijiwa's proof.



2: Paper Source PDF document

Paper's Title:

On a Class of Meromorphic Functions of Janowski Type Related with a Convolution Operator

Author(s):

Abdul Rahman S. Juma, Husamaldin I. Dhayea

Department of Mathematics,
Alanbar University, Ramadi,
Iraq.
E-mail: dr_juma@hotmail.com

Department of Mathematics,
Tikrit University, Tikrit,
Iraq.
URL: husamaddin@gmail.com

Abstract:

In this paper, we have introduced and studied new operator $Qkλ,m,γ by the Hadamard product (or convolution) of two linear operators Dkλ and Im,γ, then using this operator to study and investigate a new subclass of meromorphic functions of Janowski type, giving the coefficient bounds, a sufficient condition for a function to belong to the considered class and also a convolution property. The results presented provide generalizations of results given in earlier works.



2: Paper Source PDF document

Paper's Title:

Sweeping Surfaces with Darboux Frame in Euclidean 3-space E3

Author(s):

F. Mofarreh, R. Abdel-Baky and N. Alluhaibi

Mathematical Science Department, Faculty of Science,
Princess Nourah bint Abdulrahman University
Riyadh  11546,
Saudi Arabia.
E-mail: fyalmofarrah@pnu.edu.sa

 
Department of Mathematics, Faculty of Science,
University of Assiut,
Assiut 71516,
Egypt.
E-mail: rbaky@live.com

Department of Mathematics Science and Arts, College Rabigh Campus,
 King Abdulaziz University
Jeddah,
Saudi Arabia.
E-mail: nallehaibi@kau.edu.sa

Abstract:

The curve on a regular surface has a moving frame and it is called Darboux frame. We introduce sweeping surfaces along the curve relating to the this frame and investigate their geometrical properties. Moreover, we obtain the necessary and sufficient conditions for these surfaces to be developable ruled surfaces. Finally, an example to illustrate the application of the results is introduced.



2: Paper Source PDF document

Paper's Title:

Generalized Von Neumann-Jordan Constant for Morrey Spaces and Small Morrey Spaces

Author(s):

H. Rahman and H. Gunawan

Department of Mathematics,
Islamic State University Maulana Malik Ibrahim Malang,
Jalan Gajayana No.50,
Indonesia.
E-mail: hairur@mat.uin-malang.ac.id

Analysis and Geometry Group,
Faculty of Mathematics and Natural Sciences,
Bandung Institute of Technology, Bandung 40132,
Indonesia.
E-mail: hgunawan@math.itb.ac.id
URL:  http://personal.fmipa.itb.ac.id/hgunawan/

Abstract:

In this paper we calculate some geometric constants for Morrey spaces and small Morrey spaces, namely generalized Von Neumann-Jordan constant, modified Von Neumann-Jordan constants, and Zbaganu constant. All these constants measure the uniformly nonsquareness of the spaces. We obtain that their values are the same as the value of Von Neumann-Jordan constant for Morrey spaces and small Morrey spaces.



1: Paper Source PDF document

Paper's Title:

Multivalued Equilibrium Problems with Trifunction

Author(s):

Muhammad Aslam Noor

Etisalat College of Engineering, P.O. Box 980, Sharjah, United Arab Emirates
noor@ece.ac.ae

Abstract:

In this paper, we use the auxiliary principle technique to suggest some new classes of iterative algorithms for solving multivalued equilibrium problems with trifunction. The convergence of the proposed methods either requires partially relaxed strongly monotonicity or pseudomonotonicity. As special cases, we obtain a number of known and new results for solving various classes of equilibrium and variational inequality problems. Since multivalued equilibrium problems with trifunction include equilibrium, variational inequality and complementarity problems as specials cases, our results continue to hold for these problems.



1: Paper Source PDF document

Paper's Title:

Classes of Meromorphic p-valent Parabolic Starlike Functions with Positive Coefficients

Author(s):

S. Sivaprasad Kumar, V. Ravichandran, and G. Murugusundaramoorthy

Department of Applied Mathematics
Delhi College of Engineering,
Delhi 110042, India
sivpk71@yahoo.com

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

Department of Mathematics
Vellore Institute of Technology (Deemed University)
Vellore 632 014, India
gmsmoorthy@yahoo.com


Abstract:

In the present paper, we consider two general subclasses of meromorphic p-valent starlike functions with positive coefficients and obtain a necessary and sufficient condition for functions to be in these classes. Also we obtain certain other related results as a consequences of our main results.



1: 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.



1: Paper Source PDF document

Paper's Title:

Turan Type Inequalities for Some Special Functions

Author(s):

W. T. Sulaiman

Department of Computer Engineering,
College of Engineering,
University of Mosul,
Iraq

waadsulaiman@hotmail.com

 

Abstract:

In this paper new results concerning the q-polygamma and q-zeta functions are presented. Other generealizations of some known results are also obtained.



1: Paper Source PDF document

Paper's Title:

On the Three Variable Reciprocity Theorem and Its Applications

Author(s):

D. D. Somashekara and D. Mamta

Department of Studies in Mathematics,
University of Mysore,
Manasagangotri, Mysore-570 006
India
dsomashekara@yahoo.com 

Department of Mathematics,
The National Institute of Engineering,
Mysore-570 008,
India
mathsmamta@yahoo.com  
 

Abstract:

In this paper we show how the three variable reciprocity theorem can be easily derived from the well known two variable reciprocity theorem of Ramanujan by parameter augmentation. Further we derive some q-gamma, q-beta and eta-function identities from the three variable reciprocity theorem.



1: Paper Source PDF document

Paper's Title:

Certain Compact Generalizations of Well-Known Polynomial Inequalities

Author(s):

N. A. Rather and Suhail Gulzar

Department of Mathematics,
University of Kashmir, Hazratbal Srinagar-190006,
India.

dr.narather@gmail.com

sgmattoo@gmail.com

Abstract:

In this paper, certain sharp compact generalizations of well-known Bernstien-type inequalities for polynomials, from which a variety of interesting results follow as special cases, are obtained.



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:

Analysis of a Frictional Contact Problem for Viscoelastic Piezoelectric Materials

Author(s):

Meziane Said Ameur, Tedjani Hadj Ammar and Laid Maiza

Departement of Mathematics,
El Oued University,
P.O. Box 789, 39000 El Oued,
Algeria.
E-mail: said-ameur-meziane@univ-eloued.dz

Departement of Mathematics,
El Oued University,
P.O. Box 789, 39000 El Oued,
Algeria.
E-mail: hadjammar-tedjani@univ-eloued.dz

Department of Mathematics,
Kasdi Merbah University,
30000 Ouargla,
Algeria.
E-mail: maiza.laid@univ-ouargla.dz

 

Abstract:

In this paper, we consider a mathematical model that describes the quasi-static process of contact between two thermo-electro-viscoelastic bodies with damage and adhesion. The damage of the materials caused by elastic deformations. The contact is frictional and modeled with a normal compliance condition involving adhesion effect of contact surfaces. Evolution of the bonding field is described by a first order differential equation. We derive variational formulation for the model and prove an existence and uniqueness result of the weak solution. The proof is based on arguments of evolutionary variational inequalities, parabolic inequalities, differential equations, and fixed point theorem.


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