Browsing by Author "Sintunavarat, Wutiphol"

Now showing 1 - 6 of 6

Citation - WoS: 25
Citation - Scopus: 30
Best proximity points and extension of Mizoguchi-Takahashi's fixed point theorems
(Springer int Publ Ag, 2013) Kumam, Poom; Aydi, Hassen; Karapinar, Erdal; Sintunavarat, Wutiphol
In 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.
Citation - WoS: 29
Citation - Scopus: 30
Coupled fixed point theorems in cone metric spaces with a c-distance and applications
(Springer international Publishing Ag, 2012) Karapinar, Erdal; Kumam, Poom; Sintunavarat, Wutiphol
In 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.
Citation - WoS: 30
Citation - Scopus: 35
Discussion of Coupled and Tripled Coincidence Point Theorems for Φ-Contractive Mappings Without the Mixed g-monotone Property
(Springer international Publishing Ag, 2014) Karapinar, Erdal; Roldan, Antonio; Shahzad, Naseer; Sintunavarat, Wutiphol
After the appearance of Ran and Reuring's theorem and Nieto and Rodriguez-Lopez's theorem, the field of fixed point theory applied to partially ordered metric spaces has attracted much attention. Coupled, tripled, quadrupled and multidimensional fixed point results has been presented in recent times. One of the most important hypotheses of these theorems was the mixed monotone property. The notion of invariant set was introduced in order to avoid the condition of mixed monotone property, and many statements have been proved using these hypotheses. In this paper we show that the invariant condition, together with transitivity, lets us to prove in many occasions similar theorems to which were introduced using the mixed monotone property.
Citation - WoS: 13
Citation - Scopus: 14
The Existence of Optimal Approximate Solution Theorems for Generalized Α-Proximal Contraction Non-Self Mappings and Applications
(Springer international Publishing Ag, 2013) Karapinar, Erdal; Sintunavarat, Wutiphol
In 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.
Citation - WoS: 22
Citation - Scopus: 29
Fixed point results for generalized (α, ψ)-Meir-Keeler contractive mappings and applications
(Springeropen, 2014) Latif, Abdul; Gordji, Madjid Eshaghi; Karapinar, Erdal; Sintunavarat, Wutiphol
In this paper, we introduce a new type of a generalized-(alpha, psi)-Meir-Keeler contractive mapping and establish some interesting theorems on the existence of fixed points for such mappings via admissible mappings. Applying our results, we derive fixed point theorems in ordinary metric spaces and metric spaces endowed with an arbitrary binary relation.
Citation - WoS: 18
Citation - Scopus: 21
TRIPLED BEST PROXIMITY POINT THEOREM IN METRIC SPACES
(Element, 2013) Cho, Yeol Je; Gupta, Animesh; Karapinar, Erdal; Kumam, Poom; Sintunavarat, Wutiphol
The 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.