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7: Paper Source PDF document

Paper's Title:

On the Asymptotic Behavior of Solutions of Third Order Nonlinear Differential Equations

Author(s):

Ivan Mojsej and Alena Tartaľová

Institute of Mathematics,
Faculty of Science, P. J. Šafárik University,
Jesenná 5, 041 54 Košice,
Slovak Republic
ivan.mojsej@upjs.sk

Department of Applied Mathematics and Business Informatics,
Faculty of Economics, Technical University,
Nemcovej 32, 040 01 Košice,
Slovak Republic
alena.tartalova@tuke.sk


Abstract:

This paper is concerned with the asymptotic behavior of solutions of nonlinear differential equations of the third order with quasiderivatives. Mainly, we present the necessary and sufficient conditions for the existence of nonoscillatory solutions with specified asymptotic behavior as t tends to infinity. These conditions are presented as integral criteria and involve only the coefficients of investigated differential equations. In order to prove some of the results, we use a topological approach based on the Schauder fixed point theorem.



4: Paper Source PDF document

Paper's Title:

A Nonhomogeneous Subdiffusion Heat Equation

Author(s):

Joel-Arturo Rodriguez-Ceballos, Ana-Magnolia Marin, Ruben-Dario Ortiz

Instituto Tecnológico de Morelia,
Morelia, Michoacan,
Mexico

E-mail: joel@ifm.umich.mx

Universidad de Cartagena,
Campus San Pablo,
Cartagena de Indias, Bolivar,
Colombia

E-mail: amarinr@unicartagena.edu.co

E-mail:  joel@ifm.umich.mx

Abstract:

In this paper we consider a nonhomogeneous subdiffusion heat equation of fractional order with Dirichlet boundary conditions.



3: Paper Source PDF document

Paper's Title:

Trapping of Water Waves By Underwater Ridges

Author(s):

1A. M. Marin, 1R. D. Ortiz and 2J. A. Rodriguez-Ceballos.


1Facultad de Ciencias Exactas y Naturales
Universidad de Cartagena
Sede Piedra de Bolivar, Avenida del Consulado
Cartagena de Indias, Bolivar,
Colombia.

2Instituto Tecnológico de Morelia Facultad de Ciencias Fisico Matematicas
Universidad Michoacana Tecnológico
1500, Col. Lomas de Santiaguito Edificio Be ,
Ciudad Universitaria, 58120 Morelia, Michoacan,
Mexico.


amarinr@unicartagena.edu.co, ortizo@unicartagena.edu.co.


URL: www.unicartagena.edu.co.

Abstract:

As is well-known, underwater ridges and submerged horizontal cylinders can serve as waveguides for surface water waves. For large values of the wavenumber in the direction of the ridge, there is only one trapped wave (this was proved in Bonnet & Joly (1993, SIAM J. Appl. Math. 53, pp 1507-1550)).
We construct the asymptotics of these trapped waves and their frequencies at high frequency by means of reducing the initial problem to a pair of boundary integral equations and then by applying the method of Zhevandrov & Merzon (2003, AMS Transl. (2) 208, pp 235-284), in order to solve them.



3: Paper Source PDF document

Paper's Title:

Solving Two Point Boundary Value Problems by Modified Sumudu Transform Homotopy Perturbation Method

Author(s):

Asem AL Nemrat and Zarita Zainuddin

School of Mathematical Sciences,
Universiti Sains Malaysia,
11800 Penang,
Malaysia.
E-mail: alnemrata@yahoo.com
zarita@usm.my

Abstract:

This paper considers a combined form of the Sumudu transform with the modified homotopy perturbation method (MHPM) to find approximate and analytical solutions for nonlinear two point boundary value problems. This method is called the modified Sumudu transform homotopy perturbation method (MSTHPM). The suggested technique avoids the round-off errors and finds the solution without any restrictive assumptions or discretization. We will introduce an appropriate initial approximation and furthermore, the residual error will be canceled in some points of the interval (RECP). Only a first order approximation of MSTHPM will be required, as compared to STHPM, which needs more iterations for the same cases of study. After comparing figures between approximate, MSTHPM, STHPM and numerical solutions, it is found through the solutions we have obtained that they are highly accurate, indicating that the MSTHPM is very effective, simple and can be used to solve other types of nonlinear boundary value problems (BVPs).



2: Paper Source PDF document

Paper's Title:

Local and Global Existence and Uniqueness Results for Second and Higher Order Impulsive Functional Differential Equations with Infinite Delay

Author(s):

Johnny Henderson and Abdelghani Ouahab

Department of Mathematics, Baylor University,
Waco, Texas 76798-7328
USA.
Johnny_Henderson@baylor.edu

Laboratoire de Mathématiques, Université de Sidi Bel Abbés
BP 89, 22000 Sidi Bel Abbées,
Algérie.
ouahab@univ-sba.dz


Abstract:

In this paper, we discuss the local and global existence and uniqueness results for second and higher order impulsive functional differential equations with infinite delay. We shall rely on a nonlinear alternative of Leray-Schauder. For the global existence and uniqueness we apply a recent Frigon and Granas nonlinear alternative of Leray-Schauder type in Fréchet spaces.



2: Paper Source PDF document

Paper's Title:

Bilinear Regular Operators on Quasi-Normed Functional Spaces

Author(s):

D. L. Fernandez and E. B. Silva

Universidade Estadual de Campinas - Unicamp
Instituto de Matematica
Campinas - SP
Brazil.
E-mail: dicesar@ime.unicamp.br

Universidade Estadual de Maringa--UEM
Departamento de Matematica
Av.~Colombo 5790
Maringa - PR
Brazil.
E-mail: ebsilva@uem.br

Abstract:

Positive and regular bilinear operators on quasi-normed functional spaces are introduced and theorems characterizing compactness of these operators are proved. Relations between bilinear operators and their adjoints in normed functional spaces are also studied.



1: Paper Source PDF document

Paper's Title:

A Majorization Problem for the Subclass of p-Valently Analytic Functions of Complex Order

Author(s):

Sezgin Akbulut

Department of Mathematics, Science and Art Faculty,
Atatürk University, 25240 Erzurum, Turkey
sbulut@atauni.edu.tr

Abstract:

The main purpose of this paper is to investigate a majorization problem for the class . Relevant connections of the main result obtained in this paper with those given by earlier workers on the subject are also pointed out.



1: Paper Source PDF document

Paper's Title:

Komatu Integral Transforms of Analytic Functions Subordinate to Convex Functions

Author(s):

T. N. Shanmugam and C. Ramachandran

Department of Mathematics, College of Engineering,
Anna University, Chennai-600 025, Tamilnadu,
India
shan@annauniv.edu

Department of Mathematics, College of Engineering,
Anna University, Chennai-600 025, Tamilnadu,
India
crjsp2004@yahoo.com


Abstract:

In this paper, we consider the class A of the functions f(z) of the form


which are analytic in an open disk and study certain subclass of the class A, for which

has some property. Certain inclusion and the closure properties like convolution with convex univalent function etc. are studied.



1: Paper Source PDF document

Paper's Title:

A Coefficient Inequality For Certain Subclasses of Analytic Functions Related to Complex Order

Author(s):

B. Srutha Keerthi, B. Adolf Stephen and S. Sivasubramanian

Department Of Applied Mathematics, Sri Venkateswara College Of Engineering, Anna University,
Sriperumbudur, Chennai - 602 105,
India.
laya@svce.ac.in

Department of Mathematics, Madras Christian College, Chennai - 600059,
India
adolfmcc2003@yahoo.co.in

Department of Mathematics, College of Engineering, Anna University,
Tamilnadu, Chennai - 600 025,
India.
sivasaisastha@rediffmail.com


Abstract:

In this present investigation, the authors obtain coefficient inequality for certain normalized analytic functions of complex order f(z) defined on the open unit disk for which ( and be a complex number) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions of complex order defined by convolution are given. As a special case of this result, coefficient inequality for a class of functions defined through fractional derivatives is obtained. The motivation of this paper is to give a generalization of the coefficient inequalities of the subclasses of starlike and convex functions of complex order.



1: Paper Source PDF document

Paper's Title:

Subordination Results Associated with Hadamard Product

Author(s):

S. Sivasubramanian, C. Ramachandran and B. A. Frasin

Department of Mathematics,
University College of Engineering,
Anna University,
Saram-604 307,
India

sivasaisastha@rediffmail.com

Department of Mathematics,
University College of Engineering,
Anna University,
Villupuram,
India

crjsp2004@yahoo.com

Department of Mathematics,
Al al-Bayt University,
P.O. Box: 130095 Mafraq,
Jordan

bafrasin@yahoo.com


 

Abstract:

In the present investigation, we consider an unified class of functions of complex order using Hadamard's convolution. We obtain a necessary and sufficient condition for functions to be in these classes.



1: Paper Source PDF document

Paper's Title:

MSplit Equality for Monotone Inclusion Problem and Fixed Point Problem in Real Banach Spaces

Author(s):

1,2Christian Chibueze Okeke, 3Abdumalik Usman Bello, 1Chinedu Izuchukwu, and 1Oluwatosin Temitope Mewomo

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

2DST-NRF Center of Excellence in Mathematical and Statistical Sciences (CoE-Mass)
Johannesburg,
South Africa.

3Federal University,
Dutsin-Ma, Katsina State,
Nigeria.
E-mail: uabdulmalik@fudutsinma.edu.ng

Abstract:

In this paper a new iterative algorithm for approximating a common solution of split equality monotone inclusion problem and split equality fixed point problem is introduced. Using our algorithm, we state and prove a strong convergence theorem for approximating an element in the intersection of the set of solutions of a split equality monotone inclusion problem and the set of solutions of a split equality fixed point problem for right Bregman strongly nonexpansive mappings in the setting of p-uniformly convex Banach spaces which are also uniformly smooth. We also give some applications.



1: Paper Source PDF document

Paper's Title:

Fractional class of analytic functions Defined Using q-Differential Operator

Author(s):

K . R. Karthikeyan, Musthafa Ibrahim and S. Srinivasan

Department of Mathematics and Statistics,
Caledonian College of Engineering, Muscat,
Sultanate of Oman.
E-mail: kr_karthikeyan1979@yahoo.com

College of Engineering,
University of Buraimi, Al Buraimi,
Sultanate of Oman.
E-mail: musthafa.ibrahim@gmail.com

Department of Mathematics, Presidency College (Autonomous),
Chennai-600005, Tamilnadu,
India.
 

Abstract:

We define a q-differential fractional operator, which generalizes Salagean and Ruscheweyh differential operators. We introduce and study a new class of analytic functions involving q-differential fractional operator. We also determine the necessary and sufficient conditions for functions to be in the class. Further, we obtain the coefficient estimates, extreme points, growth and distortion bounds.



1: Paper Source PDF document

Paper's Title:

A Multivalued Version of the Radon-Nikodym Theorem, via the Single-valued Gould Integral

Author(s):

Domenico Candeloro1, Anca Croitoru2, Alina Gavriluţ2, Anna Rita Sambucini1

1Dept. of Mathematics and Computer Sciences,
University of Perugia,
1, Via Vanvitelli -- 06123, Perugia,
Italy.
E-mail:  domenico.candeloro@unipg.it, anna.sambucini@unipg.it

2Faculty of Mathematics,
Al. I. Cuza University,
700506 Iaşi,
Romania.
E-mail: croitoru@uaic.ro, gavrilut@uaic.ro

Abstract:

In this paper we consider a Gould type integral of real functions with respect to a compact and convex valued not necessarily additive measure. In particular we will introduce the concept of integrable multimeasure and, thanks to this notion, we will establish an exact Radon-Nikodym theorem relative to a fuzzy multisubmeasure which is new also in the finite dimensional case. Some results concerning the Gould integral are also obtained.



1: Paper Source PDF document

Paper's Title:

Iterative Algorithm for Split Generalized Mixed Equilibrium Problem Involving Relaxed Monotone Mappings in Real Hilbert Spaces

Author(s):

1U.A. Osisiogu, F.L. Adum, and 2C. Izuchukwu

1Department of Mathematics and Computer Science,
Ebonyi State University, Abakaliki,
Nigeria.
E-mail: uosisiogu@gmail.com, adumson2@yahoo.com

2School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal, Durban,
South Africa.
E-mail: izuchukwuc@ukzn.ac.za, izuchukwu_c@yahoo.com

Abstract:

The main purpose of this paper is to introduce a certain class of split generalized mixed equilibrium problem involving relaxed monotone mappings. To solve our proposed problem, we introduce an iterative algorithm and obtain its strong convergence to a solution of the split generalized mixed equilibrium problems in Hilbert spaces. As special cases of the proposed problem, we studied the proximal split feasibility problem and variational inclusion problem.



1: Paper Source PDF document

Paper's Title:

A Low Order Least-Squares Nonconforming Finite Element Method for Steady Magnetohydrodynamic Equations

Author(s):

Z. Yu, D. Shi and H. Zhu

College of Science,
Zhongyuan University of Technology,
Zhengzhou 450007,
China.
E-mail: 5772@zut.edu.cn

School of Mathematics and Statistics,
Zhengzhou University,
Zhengzhou 450001,
China.
E-mail: shi_dy@126.com

Mathematics Department,
University of Southern Mississippi,
Hattiesburg MS, 39406,
U.S.A
E-mail: huiqing.zhu@usm.edu

Abstract:

A low order least-squares nonconforming finite element (NFE) method is proposed for magnetohydrodynamic equations with EQ1rot element and zero-order Raviart-Thomas element. Based on the above element's typical interpolations properties, the existence and uniqueness of the approximate solutions are proved and the optimal order error estimates for the corresponding variables are derived.



1: Paper Source PDF document

Paper's Title:

The Effect of Harvesting Activities on Prey-Predator Fishery Model with Holling type II in Toxicant Aquatic Ecosystem

Author(s):

Moh Nurul Huda, Fidia Deny Tisna Amijaya, Ika Purnamasari

Department of Mathematics, Faculty of Mathematics and Natural Science,
Mulawarman University,
Samarinda, East Kalimantan,75123
Indonesia.
E-mail: muh.nurulhuda@fmipa.unmul.ac.id
 fidiadta@fmipa.unmul.ac.id
ika.purnamasari@fmipa.unmul.ac.id

Abstract:

This paper discussed prey-predator fishery models, in particular by analysing the effects of toxic substances on aquatic ecosystems. It is assumed in this model, that the prey population is plankton and the predator population is fish.\ Interaction between the two populations uses the Holling type II function. The existence of local and global critical points of the system are shown and their stability properties are analysed. Furthermore, Bionomic equilibrium and optimal control of harvesting are discussed. Finally, numerical simulations have been carried out to show in the interpretation of results.



1: Paper Source PDF document

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.


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