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Halpern-type iterative process for solving split common fixed point and monotone variational inclusion problem between Banach spaces

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Abstract

In this paper, we study the split common fixed point and monotone variational inclusion problem in uniformly convex and 2-uniformly smooth Banach spaces. We propose a Halpern-type algorithm with two self-adaptive stepsizes for obtaining solution of the problem and prove strong convergence theorem for the algorithm. Many existing results in literature are derived as corollary to our main result. In addition, we apply our main result to split common minimization problem and fixed point problem and illustrate the efficiency and performance of our algorithm with a numerical example. The main result in this paper extends and generalizes many recent related results in the literature in this direction.

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Acknowledgements

The authors sincerely thank the anonymous reviewers for their careful reading, constructive comments, and fruitful suggestions that substantially improved the manuscript.

Funding

The first author acknowledges with thanks the International Mathematical Union Breakout Graduate Fellowship (IMU-BGF) Award for his doctoral study. The third author is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903). Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the IMU and NRF.

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  1. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

    A. Taiwo, T. O. Alakoya & O. T. Mewomo

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  1. A. Taiwo
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  3. O. T. Mewomo
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Correspondence to O. T. Mewomo.

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Taiwo, A., Alakoya, T.O. & Mewomo, O.T. Halpern-type iterative process for solving split common fixed point and monotone variational inclusion problem between Banach spaces. Numer Algor 86, 1359–1389 (2021). https://doi.org/10.1007/s11075-020-00937-2

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