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Article Citation - WoS: 16Citation - Scopus: 17A Generalized Meir-Keeler Contraction on Partial Metric Spaces(Hindawi Ltd, 2012) Aydi, Hassen; Karapinar, Erdal; Rezapour, Shahram; Karapnar, ErdalWe introduce a generalization of the Meir-Keeler-type contractions, referred to as generalized Meir-Keeler-type contractions, over partial metric spaces. Moreover, we show that every orbitally continuous generalized Meir-Keeler-type contraction has a fixed point on a 0-complete partial metric space.Article Citation - WoS: 25Citation - Scopus: 36Fixed Point Results for Α-ψλ-contractions on Gauge Spaces and Applications(Hindawi Publishing Corporation, 2013) Jleli, Mohamed; Karapinar, Erdal; Samet, Bessem; Karapnar, ErdalWe extend the concept of alpha-psi-contractive mappings introduced recently by Samet et al. (2012) to the setting of gauge spaces. New fixed point results are established on such spaces, and some applications to nonlinear integral equations on the half-line are presented.Editorial Advances on Multivalued Operators and Related Fixed Point Problems(Hindawi Publishing Corporation, 2014) Chen, Chi-Ming; Karapinar, Erdal; Du, Wei-Shih; Aydi, Hassen; Romaguera, Salvador; Karapnar, Erdal[No Abstract Available]Article Citation - WoS: 9Citation - Scopus: 13Best Proximity Point Results for Mk-Proximal Contractions(Hindawi Publishing Corporation, 2012) Jleli, Mohamed; Karapinar, Erdal; Samet, Bessem; Karapnar, ErdalLet 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.Article Citation - WoS: 122Citation - Scopus: 347Generalized Α-Ψ Contractive Type Mappings and Related Fixed Point Theorems With Applications(Hindawi Publishing Corporation, 2012) Karapinar, Erdal; Samet, Bessem; Karapnar, ErdalWe establish fixed point theorems for a new class of contractive mappings. As consequences of our main results, we obtain fixed point theorems on metric spaces endowed with a partial order and fixed point theorems for cyclic contractive mappings. Various examples are presented to illustrate our obtained results.Article Citation - WoS: 33Citation - Scopus: 31Discussion on "multidimensional Coincidence Points" Via Recent Publications(Hindawi Ltd, 2014) Al-Mezel, Saleh A.; Alsulami, Hamed H.; Karapinar, Erdal; Lopez-de-Hierro, Antonio-Francisco Roldan; Karapnar, ErdalWe show that some definitions of multidimensional coincidence points are not compatible with the mixed monotone property. Thus, some theorems reported in the recent publications (Dalal et al., 2014 and Imdad et al., 2013) have gaps. We clarify these gaps and we present a new theorem to correct the mentioned results. Furthermore, we show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem.Article Citation - WoS: 5Citation - Scopus: 9On Weakly (c, Ψ, Φ)-Contractive Mappings in Ordered Partial Metric Spaces(Hindawi Publishing Corporation, 2012) Karapinar, Erdal; Shatanawi, Wasfi; Karapnar, ErdalWe introduce the notion of weakly (C, psi, phi)-contractive mappings in ordered partial metric spaces and prove some common fixed point theorems for such contractive mappings in the context of partially ordered partial metric spaces under certain conditions. We give some common fixed point results of integral type as an application of our main theorem. Also, we give an example and an application of integral equation to support the useability of our results.Article Citation - WoS: 15Citation - Scopus: 21A Best Proximity Point Result in Modular Spaces with the Fatou Property(Hindawi Ltd, 2013) Jleli, Mohamed; Karapinar, Erdal; Samet, Bessem; Karapnar, ErdalConsider a nonself-mapping T: A -> B, where (A, B) is a pair of nonempty subsets of a modular space. X-rho. A best proximity point of T is a point z is an element of A satisfying the condition: rho(z - Tz) = inf {rho(x-y) : (x,y) is an element of A x B}. In this paper, we introduce the class of proximal quasicontraction nonself-mappings in modular spaces with the Fatou property. For such mappings, we provide sufficient conditions assuring the existence and uniqueness of best proximity points.
