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Article Citation - WoS: 12Citation - Scopus: 21On Some Fixed Point Theorems Under (α, Ψ, Φ)-Contractivity Conditions in Metric Spaces Endowed With Transitive Binary Relations(Springer international Publishing Ag, 2015) Shahzad, Naseer; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-FranciscoAfter the appearance of Nieto and Rodriguez-Lopez's theorem, the branch of fixed point theory devoted to the setting of partially ordered metric spaces have attracted much attention in the last years, especially when coupled, tripled, quadrupled and, in general, multidimensional fixed points are studied. Almost all papers in this direction have been forced to present two results assuming two different hypotheses: the involved mapping should be continuous or the metric framework should be regular. Both conditions seem to be different in nature because one of them refers to the mapping and the other one is assumed on the ambient space. In this paper, we unify such different conditions in a unique one. By introducing the notion of continuity of a mapping from a metric space into itself depending on a function alpha, which is the case that covers the partially ordered setting, we extend some very recent theorems involving control functions that only must be lower/upper semi-continuous from the right. Finally, we use metric spaces endowed with transitive binary relations rather than partial orders.Book Part Kinetics of Co2 Capture by Carbon Dioxide Binding Organic Liquids(Springer international Publishing Ag, 2016) Orhan, Ozge Yuksel; Kayi, Hakan; Alper, Erdogan[No Abstract Available]Article Citation - WoS: 51Citation - Scopus: 57Tripled Coincidence Point Results for Generalized Contractions in Ordered Generalized Metric Spaces(Springer international Publishing Ag, 2012) Aydi, Hassen; Karapinar, Erdal; Shatanawi, WasfiIn this paper, we establish some tripled coincidence point results for a mixed g-monotone mapping F : X (3) -> X satisfying (psi, I center dot)-contractions in ordered generalized metric spaces. Also, an application and some examples are given to support our results.Conference Object Citation - WoS: 2The Limit q-bernstein Operators With Varying q(Springer international Publishing Ag, 2019) Almesbahi, Manal Mastafa; Ostrovska, Sofiya; Turan, Mehmet[No Abstract Available]Article Citation - WoS: 28Citation - Scopus: 33Coincidence Point Theorems in Quasi-Metric Spaces Without Assuming the Mixed Monotone Property and Consequences in g-metric Spaces(Springer international Publishing Ag, 2014) Roldan-Lopez-de-Hierro, Antonio-Francisco; Karapinar, Erdal; de la Sen, ManuelIn this paper, we present some coincidence point theorems in the setting of quasi-metric spaces that can be applied to operators which not necessarily have the mixed monotone property. As a consequence, we particularize our results to the field of metric spaces, partially ordered metric spaces and G-metric spaces, obtaining some very recent results. Finally, we show how to use our main theorems to obtain coupled, tripled, quadrupled and multidimensional coincidence point results.Conference Object Citation - WoS: 5Advances on Fixed Point Results on Partial Metric Spaces(Springer international Publishing Ag, 2019) Karapinar, Erdal; Tas, Kenan; Rakocevic, Vladimir[No Abstract Available]Book Part Citation - WoS: 1Citation - Scopus: 2A Fixed Point Result on the Interesting Abstract Space: Partial Metric Spaces(Springer international Publishing Ag, 2019) Karapinar, ErdalIn this chapter, we shall investigate the existence of fixed point of certain mappings via simulation functions in the framework of an interesting abstract space, namely, partial metric spaces. The main results of this manuscript not only extend, but also generalize, improve and unify several existing results on the literature of metric fixed point theory.Article Citation - WoS: 57Citation - Scopus: 57Quasicone Metric Spaces and Generalizations of Caristi Kirk's Theorem(Springer international Publishing Ag, 2009) Abdeljawad, Thabet; Karapinar, ErdalCone-valued lower semicontinuous maps are used to generalize Cristi-Kirik's fixed point theorem to Cone metric spaces. The cone under consideration is assumed to be strongly minihedral and normal. First we prove such a type of fixed point theorem in compact cone metric spaces and then generalize to complete cone metric spaces. Some more general results are also obtained in quasicone metric spaces. Copyright (C) 2009 T. Abdeljawad and E. Karapinar.Article Citation - WoS: 7Citation - Scopus: 9Edelstein Type Fixed Point Theorems(Springer international Publishing Ag, 2012) Karapinar, ErdalIn this manuscript, we investigate certain conditions that imply the existence of fixed points for almost contraction mappings defined on compact metric spaces. Furthermore we introduce a criteria establishing the uniqueness of fixed points for the mentioned operators. As a result we obtain generalized results by unifying some recent related fixed point theorems on the topic.Article Citation - WoS: 37Citation - Scopus: 42Fixed Point Results for -Contractive Mappings for a Generalized Altering Distance(Springer international Publishing Ag, 2013) Berzig, Maher; Karapinar, ErdalIn this manuscript, we extend the concept of altering distance, and we introduce a new notion of -contractive mappings. We prove the existence and uniqueness of a fixed point for such mapping in the context of complete metric space. The presented theorems of this paper generalize, extend and improve some remarkable existing results in the literature. We also present several applications and consequences of our results.
