Common fixed points for a class of commuting mappings on an interval

Common Periodic Points for a Class of Continuous Commuting Mappings on an Interval

The existence of common periodic points for a family of continuous commuting self-mappings on an interval is proved and two illustrative examples are given in support of our theorem and definition. 1. Introduction and preliminaries. All mappings considered here are assumed to be continuous from the interval I = [u, v] to itself. Let F(f) and P (f) be the set of fixed and periodic points of f , ...

Common Fixed Points and Invariant Approximations for Cq-commuting Generalized nonexpansive mappings

Some common fixed point theorems for Cq-commuting generalized nonexpansive mappings have been proved in metric spaces. As applications, invariant approximation results are also obtained. The results proved in the paper extend and generalize several known results including those of M. Abbas and J.K. Kim [Bull. Korean Math. Soc. 44(2007) 537-545], I. Beg, N. Shahzad and M. Iqbal [Approx. Theory A...

Common Fixed Points of Two Commuting Mappings in Complete Metric Spaces

On Common Fixed Points of Weakly Commuting Mappings and Set - Valued Mappings

ABS]RACT. 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. 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], l...

Common fixed points for a pair of commuting mappings in complete cone metric spaces

This paper is devoted to prove the S. L. Singh’s common fixed point Theorem for commuting mappings in cone metric spaces. In this framework, we introduce the notions of generalized Kannan contraction, generalized Zamfirescu contraction and generalized Weak contraction for a pair of mappings, proving afterward fixed point results.