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Convergence theorems for G-nonexpansive mappings in convex metric spaces with a directed graph

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Abstract

We propose the modified Picard–Mann hybrid iterative process for two G-nonexpansive mappings and prove some interesting theorems in the framework of convex metric space endowed with a directed graph. We prove with some numerical examples that our proposed iterative process converges faster than all of Mann, Ishikawa and Noor iterations. Our results generalize and extend several known results to convex metric space endowed with a directed graph, including the results of Khan (Fixed Point Theory Appl 2013:69, 2013).

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Acknowledgements

The author wish to thank the editor and the referees for their comments and suggestions. The author’s research is supported by the Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan through grant number: ASSMS/2018-2019/452.

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  1. Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, P.M.B. 1526, Owerri, Imo State, Nigeria

    Godwin Amechi Okeke

  2. Abdus Salam School of Mathematical Sciences, Government College University, Lahore, 54600, Pakistan

    Godwin Amechi Okeke

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Correspondence to Godwin Amechi Okeke.

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Okeke, G.A. Convergence theorems for G-nonexpansive mappings in convex metric spaces with a directed graph. Rend. Circ. Mat. Palermo, II. Ser 70, 907–922 (2021). https://doi.org/10.1007/s12215-020-00535-0

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