In this paper, we define and study new strong convergence theorems of the modified Mann and the modified Ishikawa iterative scheme with errors for nonself-mappings which are total asymptotically nonexpansive in a uniformly convex Banach space.

Abstract:The purpose of this paper is to present some existence results for coupled fixed point of a .'; / contractive condition for mixed monotone operators in metric spaces endowed with a directed graph. Our results generalize the results obtained by Jain et al. in (International Journal of Analysis, Volume 2014, Article ID 586096, 9 pages). Moreover, we have an application to some integral system to support the results.

Some new coupled coincidence and coupled common fixed point theorems for ϕ − ψ−contraction mappings are established. We have also an application to some integral system to support the results.

We establish new fixed point theorems in 0-complete ordered partial metric spaces. Also, we give remark on coupled generalized Banach contraction. Some examples illustrate the usability of our results. The theorems presented in this paper are generalizations and improvements of the several well known results in the literature.