Poom Kumam

COMMON FIXED POINT THEOREMS FOR A PAIR OF WEAKLY COMPATIBLE MAPPINGS IN FUZZY METRIC SPACES

We prove some common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces both in the sense of Kramosil and Michalek and in the sense of George and Veeramani by using the new property and give some examples. Our results improve and generalize the main results of Mihet in (Mihet, 2010) and many fixed point theorems in fuzzy metric spaces.

Generalized common fixed point theorems in complex valued metric spaces and applications

Recently, Azam et al. introduced new spaces called the complex valued metric spaces and established the existence of fixed point theorems under the contraction condition. In this article, we extend and improve the condition of contraction of the results of Azam et al. and also apply the main result to the unique common solution of system of Urysohn integral equation.Mathematics Subject Classification (2000): 47H09; 47H10.

Coupled coincidence point theorems for contractions without commutative condition in intuitionistic fuzzy normed spaces

Recently, Gordji et al. [Math. Comput. Model. 54, 1897-1906 (2011)] prove the coupled coincidence point theorems for nonlinear contraction mappings satisfying commutative condition in intuitionistic fuzzy normed spaces. The aim of this article is to extend and improve some coupled coincidence point theorems of Gordji et al. Also, we give an example of a nonlinear contraction mapping which is not applied by the results of Gordji et al., but can be applied to our results.2000 MSC: primary 47H10; secondary 54H25; 34B15.

Weak condition for generalized multi-valued (f,α,β)-weak contraction mappings☆

Abstract In 2007, Kamran [T. Kamran, Multivalued f -weakly Picard mappings, Nonlinear Anal. 67 (2007) 2289–2296] extended the notion of multi-valued mapping from weak contraction and generalized ( α , L ) -weak contraction to f -weak contraction and generalized multi-valued f -weak contraction. He also obtained some common fixed point theorems with the notion of T -weakly commuting at a coincidence point of a hybrid pair. In this paper, we can drop the condition of T -weakly commuting in Theorems 2.9 and 3.5 in [5] . We further extend the notion of generalized multi-valued f -weak contraction and introduce the notion of generalized multi-valued ( f , α , β ) -weak contraction. We also establish some coincidence and common fixed point theorems with generalized multi-valued ( f , α , β ) -weak contraction mappings. Our results extend and generalize several common fixed point theorems of many authors.

COMMON FIXED POINT THEOREM FOR HYBRID GENERALIZED MULTI-VALUED CONTRACTION MAPPINGS

Abstract In this paper, we extend a multi-valued contraction mapping to a cyclic multi-valued contraction mapping. We also establish the existence of common fixed point theorem for a cyclic multi-valued contraction mapping. Our results extend, generalize and unify Nadler’s multi-valued contraction mapping and many fixed point theorems for multi-valued mappings.

Coupled fixed point of generalized contractive mappings on partially ordered G-metric spaces

Coupled fixed point results for nonlinear contraction mappings having a mixed monotone property in a partially ordered G-metric space due to Choudhury and Maity are extended and unified. We also provide example to validate the main results in this article.Mathematics Subject classification (2000): 47H10; 54H25.

Coupled best proximity point theorem in metric Spaces

In this article the concept of coupled best proximity point and cyclic contraction pair are introduced and then we study the existence and convergence of these points in metric spaces. We also establish new results on the existence and convergence in a uniformly convex Banach spaces. Furthermore, we give new results of coupled fixed points in metric spaces and give some illustrative examples. An open problems are also given at the end for further investigation.

On α-ψ-Meir-Keeler contractive mappings

In this paper, we introduce the notion of α-ψ-Meir-Keeler contractive mappings via a triangular α-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.

Best Proximity Point Theorems for Generalized Cyclic Contractions in Ordered Metric Spaces

In this paper, we generalized a cyclic contraction on a partially ordered complete metric space. We prove some fixed point theorems as well as some theorems on the existence of best proximity points. Our results improve and extend some recent results in the previous work.

Coincidence and fixed points for contractions and cyclical contractions in partial metric spaces

We prove some coincidence and common fixed point results for three mappings satisfying a generalized weak contractive condition in ordered partial metric spaces. As application of the presented results, we give a unique fixed point result for a mapping satisfying a weak cyclical contractive condition. We also provide some illustrative examples.MSC:47H10, 54H25.