Abstract
In this paper, we introduce some new iterative algorithms for the split common solution problems for equilibrium problems and fixed point problems of nonlinear mappings. Some examples illustrating our results are also given. MSC:47J25, 47H09, 65K10.
Highlights
Throughout this paper, we assume that H is a real Hilbert space with zero vector θ, whose inner product and norm are denoted by ·, · and ·, respectively
We study the following split common solution problem (SCSP) for equilibrium problems and fixed point problems of nonlinear mappings A, T and f : (SCSP) Find p ∈ C such that p ∈ F (T) and u := Ap ∈ K which satisfies f (u, v) ≥, ∀v ∈ K
As a generalization of the equilibrium problem ( . ), finding a common solution for some equilibrium problems and fixed point problems of nonlinear operators, it has been considered in the same subset of the same space; see [ – ]
Summary
Throughout this paper, we assume that H is a real Hilbert space with zero vector θ , whose inner product and norm are denoted by ·, · and · , respectively. Let C and K be nonempty subsets of real Banach spaces E and E , respectively. The symbol EP(f ) is used to denote the set of all solutions of the problem We study the following split common solution problem (SCSP) for equilibrium problems and fixed point problems of nonlinear mappings A, T and f :. ), finding a common solution for some equilibrium problems and fixed point problems of nonlinear operators, it has been considered in the same subset of the same space; see [ – ]. Some equilibrium problems and fixed point problems of nonlinear mappings always belong to different subsets of spaces in general. The split common solution is very important for the research on generalized equilibriums problems and fixed point problems.
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