Abstract

It is our aim to prove strong convergence of a new iterative sequence to a common element of the solution set of a generalized mixed equilibrium problem; the null space of an inverse strongly monotone operator; the set of common fixed points of a countable infinite family of nonexpansive mappings; and the set of fixed points of a continuous pseudocontractive mapping. Moreover, the common element is also a unique solution of a variational inequality problem and optimality condition for a certain minimization problem. Our theorems generalize, improve, and unify several recently announced results.

Highlights

  • Let EE be a real normed space with dual EE∗. e normalized duality mapping JJ from EE to 2EE∗ is de ned by JJJJ JJ 󶁂󶁂xx∗ ∈ EE∗ ∶ 󶄁󶄁xxx xx∗󶄑󶄑 = ‖xx‖2, ‖xx‖ = 󶙱󶙱xx∗󶙱󶙱󶙱󶙱, (1)where ⟨⋅, ⋅⟩ denotes the generalized duality pairing

  • It is our aim to prove strong convergence of a new iterative sequence to a common element of the solution set of a generalized mixed equilibrium problem; the null space of an inverse strongly monotone operator; the set of common xed points of a countable in nite family of nonexpansive mappings; and the set of xed points of a continuous pseudocontractive mapping. oreover, the common element is a unique solution of a variational inequality problem and optimality condition for a certain minimization problem

  • E most important generalization of the class of nonexpansive mappings is, perhaps, the class of pseudocontractive mappings. ese mappings are intimately connected with the important class of nonlinear accretive operators. is connection will be made precise in what follows

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Summary

Research Article

A General Approximation Scheme for Solutions of Various Problems in Fixed Point Theory. It is our aim to prove strong convergence of a new iterative sequence to a common element of the solution set of a generalized mixed equilibrium problem; the null space of an inverse strongly monotone operator; the set of common xed points of a countable in nite family of nonexpansive mappings; and the set of xed points of a continuous pseudocontractive mapping. Oreover, the common element is a unique solution of a variational inequality problem and optimality condition for a certain minimization problem. Improve, and unify several recently announced results

Introduction
Main Results
FFppxx x pp xx
GGqqxx x qq xx
Since every real Hilbert space HH is a uniformly convex real

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