FIXED POINT AND WEAK COMMUTING MAPPING (original) (raw)

Few Common Fixed Point Results For Weakly Commuting Mappings

Journal of Mathematics and Computer Science, 2013

In this paper we give a common fixed point result for a mapping of f-contractive mappings, which generalize the results of Chang [2], Hadzic [4] and Sessa et.al [10]. We also extend the results of Fisher [3], Imdad and Khan [7], Iseki [6], Singh [11], Singh and Tiwari [12].

On common fixed points of weakly commuting mappings and set-valued mappings

International Journal of Mathematics and Mathematical Sciences, 1986

Our main theorem establishes the uniqueness of the common fixed point of tw set-valued mappings and of two single-valued mappings defined on a complete metric space, under a contractive condition and a weak commutativity concept. This improves a theorem of the second author. K'Y WORDS AND PHRASES. Common fixed point, set-valued mappin., weak eomutativity. 1080 AMS SUBJECT CLASSIFICATION CODES. 54H25, 47H10. Let (X,d) be a complete metric space and let B(X) be the set of all nonempty, bounded subsets of X As in [I], let (A,B) be the function defined by (A,B) sup {d(a,b) a A, b B} for all A, B in B(X). If A consists of a single point a we write 6(A,B) (a,B) and if B also consists of a single point b we write (A,B) d(a,b) It follows immediately from the definition that

FIXED POINT THEOREM FOR COMMUTING MAPPING

It can be observed that completeness of a metric space is not enough to ensure the existence of fixed point for contractive mappings. So, fixed point theorems for such mappings require further restriction on the space or extra conditions have to be imposed on mappings or some restrictions imposed on its range. Edelstein had shown that compactness of the metric space (X,d) guarantees a unique fixed point for a contractive mapping on X. In this paper,the commutative maps are used as a tool for generalizing some of the results.

A Common Fixed Point Theorem in -Metric Spaces

Fixed Point Theory and Applications, 2007

We give some new definitions of D *-metric spaces and we prove a common fixed point theorem for a class of mappings under the condition of weakly commuting mappings in complete D *-metric spaces. We get some improved versions of several fixed point theorems in complete D *-metric spaces.

11.A Focus on a Common Fixed Point Theorem using Weakly Compatible Mappings

The purpose of this paper is to present a common fixed point theorem in a metric space which generalizes the result of Bijendra Singh and M.S.Chauhan using the weaker conditions such as Weakly compatible mappings and Associated sequence in place of compatibility and completeness of the metric space.

Common fixed points of R-weakly commuting maps in generalized metric spaces

Fixed Point Theory and Applications, 2011

In this paper, using the setting of a generalized metric space, a unique common fixed point of four R-weakly commuting maps satisfying a generalized contractive condition is obtained. We also present example in support of our result. 2000 MSC: 54H25; 47H10; 54E50.

Weakly commuting mapping in linear 2-normed spaces

2021

unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract. The main idea of this paper is establishing a common fixed point theorem for four self-mappings of a complete linear 2-normed space using the weak commutating condition and A-contraction type condition and give some inclusion relations between these concepts.