Abstract
Based on the viscosity approximation method, we introduce a new cesaro mean approximation method for finding a common solution of split generalized equilibrium problem in real Hilbert spaces. Under certain conditions control on parameters, we prove a strong convergence theorem for the sequences generated by the proposed iterative scheme. Some numerical examples are presented to illustrate the convergence results. Our results can be viewed as a generalization and improvement of various existing results in the current literature.
Highlights
Based on the viscosity approximation method, we introduce a new cesàro mean approximation method for ...nding a common solution of split generalized equilibrium problem in real Hilbert spaces
Under certain conditions control on parameters, we prove a strong convergence theorem for the sequences generated by the proposed iterative scheme
Let R denote the set of all real number, H1 and H2 be real Hilbert spaces and C and Q be nonempty closed convex subset of H1 and H2, respectively
Summary
Let R denote the set of all real number, H1 and H2 be real Hilbert spaces and C and Q be nonempty closed convex subset of H1 and H2, respectively. H be a single-valued nonlinear mapping, and let M : H ! Let the set-valued mapping M : H ! [15] introduced the following split equilibrium problem (SEP ): Let F1 : C C ! The solution set of (SGEP ) is denoted by = fp 2 GEP (F1; 1) : Ap 2 GEP (F2; 2)g They considered the following iterative method: un = Tr(nF1; 1)(xn + A (Tr(nF2; 2) xn+1 = n f (xn) + nxn + Gui [21], Wang [19] and by the ongoing research in direction, we introduce and study an iterative method for approximating a common solution of SGEP ; V IP and F P P for a nonexpansive semigroup in real Hilbert spaces
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