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Article Citation - WoS: 1Citation - Scopus: 3Spectral Approach To Derive the Representation Formulae for Solutions of the Wave Equation(Hindawi Publishing Corporation, 2012) Guseinov, Gusein Sh.Using spectral properties of the Laplace operator and some structural formula for rapidly decreasing functions of the Laplace operator, we offer a novel method to derive explicit formulae for solutions to the Cauchy problem for classical wave equation in arbitrary dimensions. Among them are the well-known d'Alembert, Poisson, and Kirchhoff representation formulae in low space dimensions.Article Citation - WoS: 32Citation - Scopus: 45Fixed Point Theorems for a Class of Α-Admissible Contractions and Applications To Boundary Value Problem(Hindawi Publishing Corporation, 2014) Alsulami, Hamed H.; Gulyaz, Selma; Karapinar, Erdal; Erhan, Inci M.A class of alpha-admissible contractions defined via altering distance functions is introduced. The existence and uniqueness conditions for fixed points of such maps on complete metric spaces are investigated and related fixed point theorems are presented. The results are reconsidered in the context of partially ordered metric spaces and applied to boundary value problems for differential equations with periodic boundary conditions.Article Citation - WoS: 9Fixed Point Results for Almost Generalized Cyclic (ψ, Φ)-Weak Contractive Type Mappings With Applications(Hindawi Publishing Corporation, 2012) Jleli, Mohamed; Karapinar, Erdal; Samet, BessemWe define a class of almost generalized cyclic (psi,phi)-weak contractive mappings and discuss the existence and uniqueness of fixed points for such mappings. We present some examples to illustrate our results. Moreover, we state some applications of our main results in nonlinear integral equations.Article Citation - WoS: 3Citation - Scopus: 7Existence of Periodic Fixed Point Theorems in the Setting of Generalized Quasi-Metric Spaces(Hindawi Publishing Corporation, 2014) Chen, Chi-Ming; Karapinar, Erdal; Rakocevic, VladimirWe introduce the notions of (alpha - phi - psi)-weaker Meir-Keeler contractive mappings and (alpha - phi)- stronger Meir-Keeler contractive mappings. We discuss the existence of periodic points in the setting of generalized quasi-metric spaces. Our results improve, extend, and generalize several results in the literature.Article Citation - WoS: 18Oscillation of Second-Order Neutral Delay and Mixed-Type Dynamic Equations on Time Scales(Hindawi Publishing Corporation, 2006) Sahiner, Y.We consider the equation (r(t)(y(Delta)(t))(gamma))(Delta) + f (t, x(delta(t))) = 0, t is an element of T, where y(t) = x(t) + p(t) x(t(t)) and. is a quotient of positive odd integers. We present some sufficient conditions for neutral delay and mixed-type dynamic equations to be oscillatory, depending on deviating arguments tau(t) and delta(t), t is an element of T. Copyright (c) 2006 Y. Sahiner.Article Citation - WoS: 9Citation - Scopus: 13Best Proximity Point Results for Mk-Proximal Contractions(Hindawi Publishing Corporation, 2012) Jleli, Mohamed; Karapinar, Erdal; Samet, BessemLet A and B be nonempty subsets of a metric space with the distance function d, and T : A -> B is a given non-self-mapping. The purpose of this paper is to solve the nonlinear programming problem that consists in minimizing the real-valued function x bar right arrow. d (x, Tx), where T belongs to a new class of contractive mappings. We provide also an iterative algorithm to find a solution of such optimization problems.Editorial Citation - Scopus: 1Approximation Theory and Numerical Analysis(Hindawi Publishing Corporation, 2014) Ostrovska,S.; Berdysheva,E.; Nowak,G.; Özban,A.Y.[No abstract available]Article Citation - WoS: 10Citation - Scopus: 11Fixed Point Theorems Via Auxiliary Functions(Hindawi Publishing Corporation, 2012) Karapinar, Erdal; Salimi, PeymanWe prove new fixed point theorems in the framework of partially ordered metric spaces. The main result is an extension and a generalization of many existing results in the literature. An example is also considered to illustrate the main result.Article Citation - WoS: 1Citation - Scopus: 18Periodic Points of Weaker Meir-Keeler Contractive Mappings on Generalized Quasimetric Spaces(Hindawi Publishing Corporation, 2014) Lin, Ing-Jer; Chen, Chi-Ming; Karapinar, ErdalBy using the weaker Meir-Keeler function phi and the triangular alpha-admissible mapping alpha, we introduce the notion of (alpha - phi)-weaker Meir-Keeler contractive mappings and prove a theorem which assures the existence of a periodic point for these mappings on generalized quasimetric spaces.Article Citation - Scopus: 1Imperative Remarks for "on Common Coupled Fixed Point Theorems for Comparable Mappings in Ordered Partially Metric Spaces" and an Answer To the Question: How To Smooth It Away(Hindawi Publishing Corporation, 2015) Alsulami,H.H.; Karapinar,E.; Roldán Lpez De Hierro,A.F.We show that the main result in the work by Mutlu et al. is not true. We explain point by point some of its main mistakes and we propose an alternative version to smooth away the defects of it. © 2015 Hamed H. Alsulami et al.
