Mizoguchi-Takahashi’s type common fixed point theorems without T-weakly commuting condition and invariant approximations (original) (raw)

Mizoguchi–Takahashi’s type common fixed point theorem

Journal of the Egyptian Mathematical Society, 2014

Recently Kamran extended the result of Mizoguchi and Takahashi for closed multivalued mappings and proved a fixed point theorem. In this paper we further extend the result concluded by Kamran and prove a common fixed point theorem by using the concept of lower semi-continuity.

An integral type fixed point theorem for multi-valued mappings employing strongly tangential property

Journal of the Egyptian Mathematical Society, 2014

Sintunavarat and Kumam (W. Sintunavarat, P. Kumam, Gregus-type common fixed point theorems for tangential multi-valued mappings of integral type in metric spaces, Int. J. Math. Math. Sci. 2011 12 (Article ID 923458)) extended the tangential property to hybrid pair of mappings which generalizes the idea of tangential property due to Pathak and Shahzad (H.K. Pathak, N. Shahzad, Gregus type fixed point results for tangential mappings satisfying contractive conditions of integral type, Bull. Belg. Math. Soc. Simon Stevin 16(2) (2009) 277-288). In the present paper, we introduce the notion of strong tangential property and utilize the same to prove an integral type metrical common fixed point theorem for non-self mappings. An illustrative example is also furnished to support our main result. Our results are corrected, improved and generalized versions of a multitude of relevant common fixed point theorems of the existing literature.

A common fixed point theorem for a commuting family of nonexpansive mappings one of which is multivalued

Fixed Point Theory and Applications, 2011

Bruck [Pac. J. Math. 53, 59-71 1974 Theorem 1] proved that for a nonempty closed convex subset E of a Banach space X, if E is weakly compact or bounded and separable and suppose that E has both (FPP) and (CFPP), then for any commuting family S of nonexpansive self-mappings of E, the set F(S) of common fixed points of S is a nonempty nonexpansive retract of E. In this paper, we extend the above result when one of its elements in S is multivalued. The result extends previously known results (on common fixed points of a pair of single valued and multivalued commuting mappings) to infinite number of mappings and to a wider class of spaces.

Fixed point theorems for multi-valued mappings obtained by altering distances

Mathematical and Computer Modelling, 2011

a b s t r a c t Recently T. Suzuki showed that the Mizoguchi-Takahashi fixed point theorem is a real generalization of Nadler's fixed point theorem. Taking inspiration from the result of Mizoguchi and Takahashi and using the ideas of Feng and Liu, Klim and Wardowski obtained some fixed point theorems and showed that their results are different from the Reich point theorem and the Mizoguchi-Takahashi fixed point theorem. Very recently, Pathak and Shahzad introduced a class of functions and generalized some fixed point theorems of Klim and Wardowski by altering distances, i.e., via the mapping T (from a complete metric space (X, d) to the class of nonempty closed subsets of X ). In this paper we introduce a new class of functions which is a subclass of the class introduced by Pathak and Shahzad and improve some results of Pathak and Shahzad by allowing T to have values in closed subsets of X .

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.

New common fixed point theorems for multivalued maps

Applied General Topology, 2014

Common fixed point theorems for a new class of multivalued maps are obtained, which generalize and extend classical fixed point theorems of Nadler and Reich and some recent Suzuki type fixed point theorems.

A Common Fixed Point Theorem for a Pair of Nonself Multi-valued Mappings

2012

A common fixed point theorem for a pair of nonself multi-valued mappings in complete metrically convex metric spaces is proved which generalizes some earlier known results due to Khan et al. [9], Bianchini [2], Chatterjea [3], Khan et al. [10] and others. An illustrative example is also discussed.