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

On Common Fixed Points, Periodic Points, and Recurrent Points of Continuous Functions

It is known that two commuting continuous functions on an interval need not have a common fixed point. However, it is not known if such two functions have a common periodic point. We had conjectured that two commuting continuous functions on an interval will typically have disjoint sets of periodic points. In this paper, we first prove that S is a nowhere dense subset of [0,1] if and only if {f...

Common Fixed Points of Two Commuting Mappings in Complete Metric Spaces

Approximation of fixed points for a continuous representation of nonexpansive mappings in Hilbert spaces

This paper introduces an implicit scheme for a   continuous representation of nonexpansive mappings on a closed convex subset of a Hilbert space with respect to a   sequence of invariant means defined on an appropriate space of bounded, continuous real valued functions of the semigroup.   The main result is to    prove the strong convergence of the proposed implicit scheme to the unique solutio...

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...

Some notes on ``Common fixed point of two $R$-weakly commuting mappings in $b$-metric spaces"

Very recently, Kuman et al. [P. Kumam, W. Sintunavarat, S. Sedghi, and N. Shobkolaei. Common Fixed Point of Two $R$-Weakly Commuting Mappings in $b$-Metric Spaces. Journal of Function Spaces, Volume 2015, Article ID 350840, 5 pages] obtained some interesting common fixed point results for two mappings satisfying generalized contractive condition in $b$-metric space without the assumption of the...