Generalization of Common Fixed Point Theorems for Two Mappings (original) (raw)

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.

Common fixed point theorems for two mappings satisfying some conditions

Bulletin of the Australian Mathematical Society, 2000

In this paper, using the concept of w-distance, we first prove common fixed point theorems in a complete metric space. Then these theorems are used to improve Kannan's fixed point theorem, Ćirić's fixed point theorem, Kada, Suzuki and Takahashi's fixed point theorem and Ume's fixed point theorem.

Common fixed point theorems for compatible mappings

International Journal of Mathematics and Mathematical Sciences, 1996

In this article, the existence of a unique common fixed point of two families of compatible maps of type (P ) on a complete metric space and a common fixed point theorem for four mappings on a metric space are proved. These theorems are an improvement over the theorems generalizes Banach Fixed Point Theorems [1], Kannan Fixed Point Theorem [12], Edelstein Fixed Point Theorem [6], Boyd and Wong's Fixed Point Theorem [2], Cirić's Fixed Point Theorems [3], Das and Naik's [5], Fixed Point Theorems for at least a pair of maps of the Jungck [7], Fixed Point Theorem and Theorem 3.1 [16].

The Existence of Fixed Point Theorems via -Distance and -Admissible Mappings and Applications

Abstract and Applied Analysis, 2013

We introduce the concept of the generalized -contraction mappings and establish the existence of fixed point theorem for such mappings by using the properties of -distance and -admissible mappings. We also apply our result to coincidence point and common fixed point theorems in metric spaces. Further, the fixed point theorems endowed with an arbitrary binary relation are also derived from our results. Our results generalize the result of Kutbi, 2013, and several results in the literature.

Some new fixed point theorems in complete metric spaces

Creative Mathematics and Informatics, 2012

In this paper, we obtain some fixed point theorems for more general classes of mappings than the A−contractions of Akram et al. We also give an example of mappings satisfying our new class of contractive mappings but which does not satisfy the contractive condition of Akram et al. Our results generalize and extend the recent results of Akram et al., and unify several other classical results in the literature.

Remarks on Recent Fixed Point Theorems

Fixed Point Theory and Applications, 2010

Coincidence and fixed point theorems for a new class of contractive, nonexpansive and hybrid contractions are proved. Applications regarding the existence of common solutions of certain functional equations are also discussed.

A Common Fixed Point Theorem in Metric Space under General Contractive Condition

Journal of Applied Mathematics, 2013

We prove a common fixed point theorem for two pairs of compatible and subsequentially continuous (alternately subcompatible and reciprocally continuous) mappings satisfying a general contractive condition in a metric space. Some illustrative examples are furnished to highlight the realized improvements. Our result improves the main result of Sedghi and Shobe (2007).

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.