Few Common Fixed Point Results For Weakly Commuting Mappings (original) (raw)

FIXED POINT AND WEAK COMMUTING MAPPING

IJRET, 2012

In this paper we prove some new fixed point theorems for weak commuting mapping on complete metric space. Our results generalize several corresponding relations in metric space of weak commuting mapping

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 Fixed Point Theorem for Weakly Contractive Mappings

In this paper, we generalize the concepts of weakly Kannan, weakly Chatterjea and weakly Zamfirescu for fuzzy metric spaces. Also, we investigate Banach's fixed point theorem for the mentioned classes of functions in these spaces. Moreover, we show that the class of weakly Kannan and weakly Chatterjea maps are subclasses of the class of weakly Zamfirescu maps.

Fixed point theorems for generalized weakly contractive mappings

Nonlinear Analysis-theory Methods & Applications, 2011

In this paper, motivated and inspired by Samet et al., we introduce the notion of generalized weakly contractive mappings in metric spaces and prove the existence and uniqueness of fixed point for such mappings, and we obtain a coupled fixed point theorem in metric spaces. These theorems generalize many previously obtained fixed point results. An example is given to illustrate the main result. Finally, we give applications of our results to fixed point results in partial metric spaces.

Some results on weakly contractive maps

2011

In this paper direct proofs of some common fixed point results for two and three mappings under weak contractive conditions are given. Some of these results are improved by using different arguments of control functions. Examples are presented showing that some generalizations can not be obtained and also that our results are distinct from the existing ones. MSC(2010): Primary: 47H10; Secondary: 54H25.

Common Fixed Point Theorem of Two Mappings Satisfying a Generalized Weak Contractive Condition

International Journal of Mathematics and Mathematical Sciences, 2009

Existence of common fixed point for two mappings which satisfy a generalized weak contractive condition is established. As a consequence, a common fixed point result for mappings satisfying a contractive condition of integral type is obtained. Our results generalize, extend, and unify several well-known comparable results in literature.