An Iterative Method for a Common Solution of Generalized Mixed Equilibrium Problem and Fixed Point Problem of Nonexpansive Semigroups

Abdellah Bnouhachem () and Michael Th. Rassias
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Abdellah Bnouhachem: Ibn Zohr University, ENSA, Equipe MAISI
Michael Th. Rassias: Department of Mathematics and Engineering Sciences Hellenic Military Academy

Chapter 2 in Convex and Variational Analysis with Applications, 2026, pp 27-48 from Springer

Abstract: Abstract In this chapter, we propose an inertial iterative method for solving a common solution of generalized mixed equilibrium problem for monotone and uniformly continuous operators and fixed point of nonexpansive semigroups in real Hilbert space, which can be viewed as a refinement and improvement of some existing methods for solving a mixed equilibrium problem and fixed point problem. The strong convergence of the sequence generated by the proposed method can be guaranteed without prior knowledge of the Lipschitz constant of the operator. Since the generalized mixed equilibrium problem includes the mixed equilibrium problem, the generalized equilibrium problem and the variational inequality problem as special cases, results presented in this chapter continue to hold for these problems.

Keywords: Generalized mixed equilibrium problem; Fixed point problem; Strong convergence; Nonexpansive semigroup; Uniformly continuous; 49J30; 47H09; 47J20 (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-032-07860-5_2

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DOI: 10.1007/978-3-032-07860-5_2

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