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In this paper, we introduce and analyze a general iterative algorithm for finding a common solution of a combination of variational inequality problems, a combination of equilibria problem, and a hierarchical fixed point problem in the setting of real Hilbert space. Under appropriate conditions we derive the strong convergence results for this method. Several special cases are also discussed. Preliminary numerical experiments are included to verify the theoretical assertions of the proposed method. The results presented in this paper extend and improve some well-known results in the literature.

fixed point theory and applications

A hybrid iterative method for a combination of equilibria problem, a combination of variational inequality problems and a hierarchical fixed point problem