Shahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79527120180301Nonlinear oscillation of certain third-order neutral differential equation with distributed delay112195210.22103/jmmrc.2018.11248.1052ENSathish KumarMarappanPaavai Engineering College (Autonomous)
Paavai Institutions,
Paavai Nagar, NH-7,
Pachal -637 018.
Namakkal Dist. Tamilnadu,
India.GanesanVDepartment of Mathematics,
Aringar Anna Government Arts College, Namakkal-637002,
Tamilnadu, India.JanakiSDeputy Directorate of statistics,
Government of Tamil Nadu,
Namakkal-637003, Tamil Nadu, India.OsamaMoaazDepartment of Mathematics,
Faculty of Science,
Mansoura University,
Mansoura, 35516, Egypt.Journal Article20171118The authors obtain necessary and sufficient conditions for the existence of oscillatory solutions with a specified asymptotic behavior of solutions to a nonlinear neutral differential equation with distributed delay of third order. We give new theorems which ensure that every solution to be either oscillatory or converges to zero asymptotically. Examples dwelling upon the importance of applicability of these results.https://jmmrc.uk.ac.ir/article_1952_1113d7a76ffceca1bb350bfe145467c6.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79527120180301Some results on convergence and existence of best proximity points1324205510.22103/jmmrc.2018.10747.1045ENMarziehAhmadi BaseriYazd University0000-0003-4997-6576H.MazaheriYazd University0000-0001-8169-8655T. DNarangGuru Nanak Dev University0000-0002-8139-8019Journal Article20170809In this paper, we introduce generalized cyclic φ-contraction maps in metric spaces and give some results of best proximity points of such mappings in the setting of a uniformly convex Banach space. Moreover, we obtain convergence and existence results of proximity points of the mappings on reflexive Banach spaceshttps://jmmrc.uk.ac.ir/article_2055_9afefc52942cb83c7c1f14b2139b09ba.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79527120180301A TAXICAB VERSION OF A TRIANGLE' S APOLLONIUS CIRCLE2536207310.22103/jmmrc.2018.2073ENTemelERMİŞDepartment of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Eskişehir Osmangazi University, Eskişehir, TURKEYOzcanGelişgenDeparment of Mathematics and Computer Sciences, Faculty of Art and Sciences, Eskişehir Osmangazi University, Eskişehir, TURKEY0000-0001-7071-6758AybukeEkiciDeparment of Mathematics and Computer Sciences, Faculty of Art and Sciences, Eskişehir Osmangazi University, Eskişehir, TURKEYJournal Article20180123One of the most famous problems of classical geometry is the Apollonius' problem asks construction of a circle which is tangent to three given objects. These objects are usually taken as points, lines, and circles. This well known problem was posed by Apollonius of Perga ( about 262 - 190 B.C.) who was a Greek mathematician known as the great geometer of ancient times after Euclid and Archimedes. The Apollonius' problem can be reduced speci cally to the question \Is there the circle that touches all three excircles of given triangle and encompasses them? " when all three objects are circles. In literature, altough there are a lot of works on the solution of this question in the Euclidean plane, there is not the work on this question in different metric geometries. In this paper, we give that the conditions of existence of Apollonius taxicab circle for any triangle.https://jmmrc.uk.ac.ir/article_2073_4b86abe48d358ecf194c56c69108433e.pdfShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79527120180301Split-step finite difference schemes for solving the nonlinear Fisher Equation3755216410.22103/jmmrc.2018.12605.1069ENM.IzadiDepartment of Applied Mathematics,
Faculty of Mathematics and Computer,
Mahani Mathematical Research Center,
Shahid Bahonar University of Kerman,
Kerman, Iran.0000-0002-6116-4928Journal Article20180820In this work, we propose several simple but accurate finite difference schemes to approximate the solutions of the nonlinear Fisher equation, which describes an interaction between logistic growth and diffusion process occurring in many biological and chemical phenomena. All schemes are based upon thetime-splitting finite difference approximations.The operator splitting transforms the original problem into two subproblems: nonlinearlogistic and linear diffusion, each with its own boundary conditions. The diffusion equation is solved by three well-known stable and consistent methods while the logistic equation by a combination of method of lagging and a two-step approximation that is not only preserve positivity but also boundedness. The new proposed schemes and the previous standard schemes are testedon a range of problems with analytical solutions. A comparison showsthat the new schemes are simple, effective and very successful in solving the Fisher equation.https://jmmrc.uk.ac.ir/article_2164_c3e4035af2a1cde9f21e1ae1951ac80b.pdf