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Article Citation - WoS: 21Citation - Scopus: 23Best Proximity Points of Generalized Almost Ψ-Geraghty Contractive Non-Self(Springer international Publishing Ag, 2014) Aydi, Hassen; Karapinar, Erdal; Erhan, Inci M.; Salimi, PeymanIn this paper, we introduce the new notion of almost psi-Geraghty contractive mappings and investigate the existence of a best proximity point for such mappings in complete metric spaces via the weak P-property. We provide an example to validate our best proximity point theorem. The obtained results extend, generalize, and complement some known fixed and best proximity point results from the literature.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: 38Citation - Scopus: 48Fixed Points of Modified f-contractive Mappings in Complete Metric-Like Spaces(Hindawi Ltd, 2015) Alsulami, Hamed H.; Karapinar, Erdal; Piri, HosseinWe introduce the notion of modified F-contractive mappings in the setting of complete metric-like spaces and we investigate the existence and uniqueness of fixed point of such mappings. The presented results unify, extend, and improve several results in the related literature.Article Citation - WoS: 46Citation - Scopus: 49Fixed Point Theorems for Generalized (α* - Ψ)-Ciric Contractive Multivalued Operators in b-metric Spaces(int Scientific Research Publications, 2016) Bota, Monica-Felicia; Chifu, Cristian; Karapinar, ErdalIn this paper we introduce the notion (alpha(*) - psi)- Ciric-type contractive multivalued operator and investigate the existence and uniqueness of fixed point for such a mapping in b-metric spaces. The well-posedness of the fixed point problem and the Ulam-Hyres stability is also studied. (C) 2016 All rights reserved.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: 43Coupled Fixed Points for Meir-Keeler Contractions in Ordered Partial Metric Spaces(Hindawi Ltd, 2012) Abdeljawad, Thabet; Aydi, Hassen; Karapinar, ErdalIn this paper, we prove the existence and uniqueness of a new Meir-Keeler type coupled fixed point theorem for two mappings F : X x X -> X and g : X -> X on a partially ordered partial metric space. We present an application to illustrate our obtained results. Further, we remark that the metric case of our results proved recently in Gordji et al. (2012) have gaps. Therefore, our results revise and generalize some of those presented in Gordji et al. (2012)Article Citation - WoS: 5Citation - Scopus: 14Existence of a Solution of Integral Equations Via Fixed Point Theorem(Springeropen, 2013) Gulyaz, Selma; Karapinar, Erdal; Rakocevic, Vladimir; Salimi, PeymanIn this paper, we establish a solution to the following integral equation: u(t) = integral(T)(0) G(t, s)f(s, u(s)) ds for all t is an element of [0,T], (1) where T > 0, f : [0, T] x R -> R and G : [0, T] x [0, T] -> [0, infinity) are continuous functions. For this purpose, we also obtain some auxiliary fixed point results which generalize, improve and unify some fixed point theorems in the literature.Article Citation - WoS: 77Citation - Scopus: 81α-admissible mappings and related fixed point theorems(Springeropen, 2013) Hussain, Nawab; Karapinar, Erdal; Salimi, Peyman; Akbar, FarhanaIn this paper, we prove the existence and uniqueness of a fixed point for certain alpha-admissible contraction mappings. Our results generalize and extend some well-known results on the topic in the literature. We consider some examples to illustrate the usability of our results.Article Citation - WoS: 13Citation - Scopus: 14The Existence of Optimal Approximate Solution Theorems for Generalized Α-Proximal Contraction Non-Self Mappings and Applications(Springer international Publishing Ag, 2013) Karapinar, Erdal; Sintunavarat, WutipholIn this paper, we investigate the sufficient conditions to find a best proximity point for a certain class of non-self mappings. It is well known that optimization problems can be transformed to the problems of the existence of a best proximity point. Hence, improvement in the best proximity point theory implicitly develops the theory of optimization. Our presented results generalize, extent and improve various well-known results on the topic in the literature. In particular, we consider some applications of our results to the best proximity point theorems on a class of metric spaces endowed with an arbitrary binary relation which involves the partially ordered metric spaces.Article Citation - WoS: 16Citation - Scopus: 17A Generalized Meir-Keeler Contraction on Partial Metric Spaces(Hindawi Ltd, 2012) Aydi, Hassen; Karapinar, Erdal; Rezapour, ShahramWe 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.
