Browsing by Author "Kumam, Poom"
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Article Citation Count: 23Best proximity points and extension of Mizoguchi-Takahashi's fixed point theorems(Springer int Publ Ag, 2013) Karapınar, Erdal; Aydi, Hassen; Karapinar, Erdal; Sintunavarat, Wutiphol; MathematicsIn this paper, we introduce a multi-valued cyclic generalized contraction by extending the Mizoguchi and Takahashi's contraction for non-self mappings. We also establish a best proximity point for such type contraction mappings in the context of metric spaces. Later, we characterize this result to investigate the existence of best proximity point theorems in uniformly convex Banach spaces. We state some illustrative examples to support our main theorems. Our results extend, improve and enrich some celebrated results in the literature, such as Nadler's fixed point theorem, Mizoguchi and Takahashi's fixed point theorem.Article Citation Count: 29Coupled fixed point theorems in cone metric spaces with a c-distance and applications(Springer international Publishing Ag, 2012) Karapınar, Erdal; Kumam, Poom; Sintunavarat, Wutiphol; MathematicsIn this paper, we extend the very recent result of Sintunavarat et al. in the paper 'Coupled fixed point theorems for weak contraction mapping under F-invariant set' (Abstr. Appl. Anal. 2012:324874, 2012). In particular, we give an example of a nonlinear contraction mapping for which our result successfully detects a coupled fixed point in contrast to the result of Sintunavarat et al., which is not applied to show the existence of a coupled fixed point. As a consequence, the main results in this paper extend and unify many results in the topic of coupled fixed points including the results of Sintunavarat et al. Also, some applications of the main results are given. MSC: 54H25, 47H10.Article Citation Count: 13Coupled fixed point theorems on partially ordered G-metric spaces(Springer int Publ Ag, 2012) Erhan, İnci; Kumam, Poom; Karapınar, Erdal; MathematicsThe purpose of this paper is to extend some recent coupled fixed point theorems in the context of partially ordered G-metric spaces in a virtually different and more natural way.Article Citation Count: 8G-Metric spaces in any number of arguments and related fixed-point theorems(Springer international Publishing Ag, 2014) Karapınar, Erdal; Karapinar, Erdal; Kumam, Poom; MathematicsInspired by the notion of Mustafa and Sims' G-metric space and the attention that this kind of metric has received in recent times, we introduce the concept of a G-metric space in any number of variables, and we study some of the basic properties. Then we prove that the family of this kind of metric is closed under finite products. Finally, we show some fixed-point theorems that improve and extend some well-known results in this field.Article Citation Count: 5Irremissible stimulate on 'Unified fixed point theorems in fuzzy metric spaces via common limit range property'(Springeropen, 2014) Karapınar, Erdal; Karapinar, Erdal; Kumam, Poom; MathematicsOne of the goals of this short note is to alert researchers as regards some mistakes that appeared in a recent paper (Chauhan, Khan and Kumar in J. Inequal. Appl. 2013: 182, 2013). This entails main proofs based on a false result, which invalidates all statements. We also give a complete revision of the antecedents of this work in order to find the main reasons of the mistakes. Finally, the main aim of this note is to propose a correct, more general version of the main theorems in the paper mentioned.Article Citation Count: 3A new class of generalized contraction using P-functions in ordered metric spaces(Sciendo, 2015) Karapınar, Erdal; Karapinar, Erdal; Kumam, Poom; MathematicsIn this paper, we introduced and studied a new class of mappings in ordered metric spaces that is inspired from the concept of a P-function introduced in Chaipunya et. al. [10]. With our new class, we furnish fixed point theorems for continuous, noncontinuous, monotonic, and nonmonotonic mappings in various kinds of the ordering structures.Article Citation Count: 12A note on 'Modified proof of Caristi's fixed point theorem on partial metric spaces, Journal of Inequalities and Applications 2013, 2013:210'(Springeropen, 2013) Karapınar, Erdal; Karapinar, Erdal; Kumam, Poom; MathematicsIn this note, we emphasize that the proofs and statements of the main results of the paper 'Modified proof of Caristi's fixed point theorem on partial metric spaces' (Journal of Inequalities and Applications 2013, 2013:210) do not have any utility to use the partial metric. Hence, it has no contribution to either partial metric theory or Caristi-type fixed point problems.Article Citation Count: 171On α-ψ-Meir-Keeler contractive mappings(Springer international Publishing Ag, 2013) Karapınar, Erdal; Kumam, Poom; Salimi, Peyman; MathematicsIn this paper, we introduce the notion of alpha-psi-Meir-Keeler contractive mappings via a triangular alpha-admissible mapping. We discuss the existence and uniqueness of a fixed point of such a mapping in the setting of complete metric spaces. We state a number of examples to illustrate our results. MSC: 46N40, 47H10, 54H25, 46T99.Article Citation Count: 16TRIPLED BEST PROXIMITY POINT THEOREM IN METRIC SPACES(Element, 2013) Karapınar, Erdal; Gupta, Animesh; Karapinar, Erdal; Kumam, Poom; Sintunavarat, Wutiphol; MathematicsThe purpose of this article is to first introduce the notion of tripled best proximity point and cyclic contraction pair. We also establish the existence and convergence theorems of tripled best proximity points in metric spaces. Moreover, we apply our results to setting of uniformly convex Banach space. Finally, we obtain some results on the existence and convergence of tripled fixed point in metric spaces and give illustrative examples of our theorems.