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Algorithmic procedure for approximate solution of split problems involving various classes of mappings

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Abstract

It is our purpose in this paper to propose an algorithmic procedure for approximating common solution of split equality fixed point problems involving finite families of \(\eta\)-demimetric mappings, \(\gamma\)-inverse strongly monotone mappings, relatively quasi-nonexpansive mappings and finite family of system of equilibrium problems in uniform convex and 2-uniformly smooth spaces. This was achieved by introducing a new iterative scheme that converges strongly to common solution. The theorems obtained extend, generalize and compliment several existing results in this area of research.

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Acknowledgements

The authors would like to thank the Simons Foundation and the coordinators of Simons Foundation for Sub-Sahara Africa Nationals with base at Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Botswana, for providing financial support for the first two authors that helped them complete their postgraduate programme. We remain grateful to the reviewer(s) whose constructive criticisms and remarks helped to improve the quality of results obtained in this paper.

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Authors and Affiliations

  1. Department of Mathematics, Federal University of Technology, Owerri, Imo State, Nigeria

    N. N. Araka & E. U. Ofoedu

  2. Department of Mathematics, Nnamdi Azikiwe University, Awka, Anambra State, Nigeria

    K. O. Ibeh & E. U. Ofoedu

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  1. N. N. Araka
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Correspondence to E. U. Ofoedu.

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Communicated by S. Ponnusamy.

To the memory of Prof. Charles Ejike Chidume (1947–2021) who did a lot of work and contributed immensely towards the growth and development of many young mathematicians and researchers like us in Africa.

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Araka, N.N., Ibeh, K.O. & Ofoedu, E.U. Algorithmic procedure for approximate solution of split problems involving various classes of mappings. J Anal 31, 2297–2329 (2023). https://doi.org/10.1007/s41478-023-00565-8

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