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A parallel viscosity extragradient method for solving a system of pseudomonotone equilibrium problems and fixed point problems in Hadamard spaces

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Abstract

In this work, we study a parallel viscosity extragradient method for approximating a common solution of a finite system of pseudomonotone equilibrium problems and common fixed point problem for nonexpansive mappings in Hadamard spaces. We propose an iterative method and prove its strong convergence to an element in the intersection of the solution set of finite system of equilibrium problems and the fixed points set of nonexpansive mappings. Furthermore, we give an example in a Hadamard space which is not an Hilbert space to support the convergence theorem in the paper. This result generalizes and extends recent results in the literature.

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Acknowledgements

The authors acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University for making their facilities available for the research. O.K. Oyewole acknowledges 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.

Funding

L.O. Jolaoso is supported by the Postdoctoral research grant from the Sefako Makgatho Health Sciences University, South Africa.

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Authors and Affiliations

  1. Department of Mathematics, Usmanu Danfodiyo University Sokoto, P.M.B. 2346, Sokoto, Sokoto state, Nigeria

    Kazeem Olalekan Aremu

  2. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 94, Medunsa 0204, Ga-Rankuwa, South Africa

    Kazeem Olalekan Aremu, Lateef Olakunle Jolaoso & Maggie Aphane

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

    Olawale Kazeem Oyewole

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

    Olawale Kazeem Oyewole

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  1. Kazeem Olalekan Aremu
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  3. Maggie Aphane
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  4. Olawale Kazeem Oyewole
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All authors worked equally on the results and approved the final manuscript.

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Correspondence to Kazeem Olalekan Aremu.

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Aremu, K.O., Jolaoso, L.O., Aphane, M. et al. A parallel viscosity extragradient method for solving a system of pseudomonotone equilibrium problems and fixed point problems in Hadamard spaces. Ricerche mat 73, 819–840 (2024). https://doi.org/10.1007/s11587-021-00640-x

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