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A strong convergence algorithm for a fixed point constrained split null point problem

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Abstract

In this paper, we introduce a new algorithm with self adaptive step-size for finding a common solution of a split feasibility problem and a fixed point problem in real Hilbert spaces. Motivated by the self adaptive step-size method, we incorporate the self adaptive step-size to overcome the difficulty of having to compute the operator norm in the proposed method. Under standard and mild assumption on the control sequences, we establish the strong convergence of the algorithm, obtain a common element in the solution set of a split feasibility problem for sum of two monotone operators and fixed point problem of a demimetric mapping. Numerical examples are presented to illustrate the performance and the behavior of our method. Our result extends, improves and unifies other results in the literature.

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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. The first and second authors acknowledge with thanks the bursary and financial support from Department of Science and Technology and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DST-NRF COE-MaSS) Doctoral Bursary. The third author is supported in part 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 CoE-MaSS and NRF.

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Authors and Affiliations

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

    O. K. Oyewole, H. A. Abass & O. T. Mewomo

  2. DST-NRF Center of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), Johannesburg, South Africa

    O. K. Oyewole & H. A. Abass

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  1. O. K. Oyewole
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  2. H. A. Abass
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  3. O. T. Mewomo
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Correspondence to O. T. Mewomo.

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Oyewole, O.K., Abass, H.A. & Mewomo, O.T. A strong convergence algorithm for a fixed point constrained split null point problem. Rend. Circ. Mat. Palermo, II. Ser 70, 389–408 (2021). https://doi.org/10.1007/s12215-020-00505-6

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