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

Author

Listed:
  • Abdellah Bnouhachem

    (Ibn Zohr University, ENSA, Equipe MAISI)

  • Michael Th. Rassias

    (Department of Mathematics and Engineering Sciences Hellenic Military Academy)

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.

Suggested Citation

  • Abdellah Bnouhachem & Michael Th. Rassias, 2026. "An Iterative Method for a Common Solution of Generalized Mixed Equilibrium Problem and Fixed Point Problem of Nonexpansive Semigroups," Springer Optimization and Its Applications,, Springer.
    • Handle: RePEc:spr:spochp:978-3-032-07860-5_2
    DOI: 10.1007/978-3-032-07860-5_2
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