DOI: 10.24193/fpt-ro.2020.2.43

Authors: K.R. Kazmi, Saleem Yousuf and Rehan Ali

Abstract: In this paper, we investigate a hybrid extra-gradient iterative method to approximate the common solution of a system of unrelated generalized mixed equilibrium problems for monotone and Lipschitz continuous mappings and system of unrelated hierarchical fixed point problems for nonexpansive mappings in Hilbert space. We prove a strong convergence theorem for the sequences generated by the proposed iterative algorithm. Further, we give some consequences and applications of our main result. Finally, we discuss a numerical example to demonstrate the applicability of the iterative algorithm.

Key Words and Phrases: System of unrelated generalized mixed equilibrium problems, system of unrelated hierarchical fixed point problems, monotone mapping, Lipschitz continuous mapping, nonexpansive mapping, hybrid extra-gradient iterative method.

2010 Mathematics Subject Classification: 47H05, 47H09, 47J25, 47H10.

Published on-line: July 1st, 2020.

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