Yunus Atalan | Searcharxiv

arXiv2019

Convergence analysis for a new faster iteration method

In this paper, we introduce a new iteration method and show that this iteration method can be used to approximate fixed point of almost contraction mappings. Furthermore, we prove that the new iteration method is equivalent to both Mann iteration method and Picard-Mann hybrid iteration method and also converges faster than Picard-Mann hybrid iteration method for the class of almost contraction mappings. In addition to these we give a table and graphics for support this result. Finally, we prove a data dependence result for almost contraction mappings by using the new iteration method.

math.FA↗

arXiv2015

Existence of fixed points for condensing operators under an integral condition

Our aim in this paper is to present results of existence of fixed points for continuous operators in Banach spaces using measure of noncompactness under an integral condition. This results are generalization of results given by A. Aghajania and M. Aliaskaria which are generalization of Darbo's fixed point theorem. As application we use these results to solve an integral equations in Banach spaces.

math.FA↗