[PDF] Top 20 Hybrid extragradient method for generalized mixed equilibrium problems and fixed point problems in Hilbert space

... real Hilbert space with the inner product ·, · and the norm · , and let C be a nonempty closed convex subset of ...following generalized mixed equilibrium ... See full document

... of equilibrium problems, which is known as the generalized mixed equilibrium ...mation method for finding a common element of the set of common solutions for generalized ... See full document

... real Hilbert space whose inner product and norm are denoted by ·, · and · ...the generalized mixed equilibrium problem (GMEP) which involves finding x ∈ C such ... See full document

... other problems, for example, the complementarity problem, fixed point problem and optimization problem, which can also be written in the form of an ...several problems arising in physics, engineering, ... See full document

... of generalized mixed equilibrium problems, the set of common fixed points of a finite family of pseudo contraction mappings, and the set of solutions of the variational inequality for an inverse ... See full document

... Theorem 3.1. Let C be a nonempty closed convex subset of a real Hilbert space H. Let F be bifunction from C × C toℝ satisfying (H1)-(H5), and let : C ® ℝ ∪ {+∞} be a proper lower semicontinuous and convex ... See full document

... iterative method to prove a strong convergence theorem for finding a common element of the set of fixed points of strict pseudocontractions, the set of common solutions of the system of generalized ... See full document

... fixed point problem of finitely many nonexpansive ...Korpelevič’s extragradient method [], the hybrid steepest-descent method in [], the viscosity approximation method, and the ... See full document

... minimization problems; see, for example, 21–24 and the references ...minimization problems have a great impact and influence in the development of almost all branches of pure and applied ...the fixed ... See full document

... Let C be a nonempty closed convex subset of a real Hilbert space H. Recall that a mapping f : C → C is called contractive if there exists a constant α ∈ 0, 1 such that fx − fy ≤ αx− y for all x, y ∈ C. A ... See full document

... Banach space having the Kadec-Klee property and a Fr´echet differentiable norm, C be a nonempty closed convex subset of E, and let T be a uniformly Lipschitzian continuous and quasi-φ-asymptotically nonexpansive ... See full document

... of Hilbert spaces and Banach ...fixed point iterations which is supposed to induce the con- vergence in norm of the ...this method is that it allows one to select a particular fixed point of T ... See full document

... minimization problems; see, for example, 21–24 and the references ...minimization problems have a great impact and influence in the development of almost all branches of pure and applied ...the fixed ... See full document

... In this paper, we always assume that H is a real Hilbert space with the inner product ·, · and the norm · , and C is a nonempty, closed, and convex subset of H. R is denoted by the set of real numbers. Let ... See full document

... new extragradient method 4.2 which is mixed the iterative schemes considered in 10–12 for finding a common element of the set of common fixed points of nonexpansive mappings, the set of ... See full document

... real Hilbert space H and let Φ : C × C → R be a bifunction, where R is the set of real ...The generalized equilibrium problem GEP for Φ : C × C → R and Ψ : C → H is to find u ∈ C such ... See full document

... of equilibrium problems has played an important role in the study of a wide class of problems arising in economics, finance, transportation, network and structural analysis, elasticity and ... See full document

... The generalized mixed equilibrium problem includes fixed point problems, optimization prob- lems, variational inequality problems, Nash equilibrium problems, ... See full document

... Now we give a strong convergence result concerning Algorithm 3.1 as follows. Theorem 3.2. Let H be a real Hilbert space. Let ϕ : H → R be a lower semicontinuous and convex functional. Let Θ : H × H → R be ... See full document

... In 2010, Kohsaka and Takahashi [11, 12] introduced the following nonlinear map- ping: Let E be a smooth, strictly convex and reflexive Banach space, let j be the duality mapping of E and let C be a nonempty closed ... See full document