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.

GENERAL COMMON FIXED POINT THEOREMS ON COMPATIBLE MAPPINGS

In this paper we prove some common fixed point results on complete metric space. KEYWORDS: complete metric space,í µí±‡ − í µí±œí µí±Ÿí µí±í µí±–í µí±¡í µí±Ží µí±™í µí±™í µí±¦ complete, weakly compatible, generalized weakly contractive

Review Article - A study of some fixed point theorems for various types of maps

International Journal of Mathematics Trends and Technology, 2016

S. The theory has several rather well-defined (yet overlapping) branches. The purely topological theory as well as those topics which lie on the borderline of topology and functional analysis (e.g. those related to Leray-Schauder theory) have their roots in the celebrated theorem of L. E. J. Brouwer. This paper presents a review of the available literature on fixed point theorems for various types of maps.

Some novel fixed-point theorems in Hausdorff spaces

Journal of Applied Research and Technology, 2021

In this paper existence and uniqueness of fixed points are proved for self maps, satisfying a new contraction without assuming the compatibility and commutative property of maps. Some remarks and applications to integral type contraction are given to illustrate the importance of our results. An open problem for future research is also given.