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Iterative solution of split variational inclusion problem in a real Banach spaces

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Abstract

In this paper, we study split variational inclusion problem in real Banach spaces with a view to analyze an iterative method for obtaining a solution of the split variational inclusion problem in Banach spaces. We propose an Halpern type algorithm and with our algorithm, we state and prove a strong convergence theorem for the approximation of solution of split variational inclusion problem in the frame work of p-uniformly convex Banach spaces which are also uniformly smooth. Our results extend and complement many known related results in the literature.

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Acknowledgments

The first author acknowledge with thanks, the bursary and financial support from the 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. Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the CoE-MaSS. Also, the authors are grateful to the anonymous referees whose suggestions and comments helped to improve the final version of this paper.

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Authors and Affiliations

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

    F. U. Ogbuisi & O. T. Mewomo

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

    F. U. Ogbuisi

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  1. F. U. Ogbuisi
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  2. O. T. Mewomo
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Correspondence to O. T. Mewomo.

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Ogbuisi, F.U., Mewomo, O.T. Iterative solution of split variational inclusion problem in a real Banach spaces. Afr. Mat. 28, 295–309 (2017). https://doi.org/10.1007/s13370-016-0450-z

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  • DOI: https://doi.org/10.1007/s13370-016-0450-z

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