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In this article, by using the S-mapping and hybrid method we prove a strong convergence theorem for finding a common element of the set of fixed point problems of a finite family of κ i -strictly pseudocontractive mappings and the set of generalized equilibrium defined by Ceng et al., which is a solution of two sets of variational inequality problems. Moreover, by using our main result we have a strong convergence theorem for finding a common element of the set of fixed point problems of a finite family of κ i -strictly pseudocontractive mappings and the set of solution of a finite family of generalized equilibrium defined by Ceng et al., which is a solution of a finite family of variational inequality problems.

fixed point theory and applications

Hybrid iterative scheme for a generalized equilibrium problems, variational inequality problems and fixed point problem of a finite family of κ i -strictly pseudocontractive mappings