Abstract
In this paper, we introduce a new composite viscosity iterative algorithm and prove the strong convergence of the proposed algorithm to a common fixed point of one finite family of nonexpansive mappings and another infinite family of nonexpansive mappings, which also solves a general mixed equilibrium problem and a finite family of variational inequalities. An example is also provided in support of the main result. The main result presented in this paper improves and extends some corresponding ones in the earlier and recent literature.
Highlights
Let H be a real Hilbert space with inner product ·, · and norm ·, C be a nonempty closed convex subset of H and PC be the metric projection of H onto C
We introduce a new composite viscosity iterative algorithm for finding a common element of the solution set general mixed equilibrium problem (GMEP)(Θ, h) of GMEP ( . ), the solution set VI(C, Ak of a finite family of variational inequalities for inverse strongly monotone mappings Ak : C → H, k =, . . . , M, and the common fixed point set of one finite family of nonexpansive mappings
Our aim is to prove that the iterative algorithm converges strongly to a common fixed point of the mappings Si, Tn : C → C, i =, . . . , N, n =, . . . , which is an equilibrium point of GMEP ( . ) and a solution of a finite family of variational inequalities for inverse strongly monotone mappings Ak : C → H, k =, . . . , M
Summary
Let H be a real Hilbert space with inner product ·, · and norm · , C be a nonempty closed convex subset of H and PC be the metric projection of H onto C. ) in [ ]) Let f : C → C be a ρ-contraction and A : C → H be an α-inverse strongly monotone mapping. ), the solution set VI(C, Ak of a finite family of variational inequalities for inverse strongly monotone mappings Ak : C → H, k = , .
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