[PDF] Top 20 Strong convergence of gradient projection method for generalized equilibrium problem in a Banach space

... We denote the solution set of GEP (.) by Sol(GEP(.)). Problem (.) includes fixed point problems, optimization problems, variational inequality problems, Nash equilib- rium problems, etc. as particular cases. ... See full document

... of equilibrium problems and/or the set of fixed points of mappings and/or the set of solutions of variational inequalities) with their applications have been dis- ...some strong or weak convergence ... See full document

... a generalized equilibrium problem with a bifunction defined on the dual space of a Banach space, and we also construct an iterative procedure generated by a hybrid method ... See full document

... Huang, Strong convergence theorems for fixed point problems and generalized equilibrium problems of three relatively quasi-nonexpansive mappings in Banach spaces, J.. Zhou, Approximate p[r] ... See full document

... Definition 2.1 see 10. Let E be a Banach space with the dual space E ∗ and let K be a nonempty subset of E. Let T : K → E ∗ and η : K × K → E be two mappings. The mapping T : K → E ∗ is said to be ... See full document

... The generalized variational inequalities find application in economics and transporta- tion equilibrium, engineering sciences, ...extra-gradient method [, ] is a popular solu- tion ... See full document

... extragradient-like method for finding a common element of the set of common fixed points of a finite family of nonexpansive mappings, the set of solutions of variational inequalities for a strongly positive linear ... See full document

... The equilibrium problem is very general in the sense that it includes, as special cases, optimization problems, variational inequal- ity problems, min-max problems, saddle point problem, fixed point ... See full document

... real Banach space with the dual space B ∗ ...a generalized mixed equilibrium problem with perturbation for short, GMEPP which includes as a special case the general mixed ... See full document

... investigate generalized asymptoti- cally quasi-φ-nonexpansive mappings and problem ...A strong convergence theorem for common solutions to a fixed point problem of generalized ... See full document

... hybrid projection method is constructed. Strong convergence of the iterative process to a common element of the set of common fixed points of a finite family of generalized nonexpansive ... 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 mixed ... See full document

... the problem of extending Theorem MYX to a Banach ...of Banach spaces, the problem of mod- ifying the Halpern iteration by hybrid projection algorithms such that strong ... See full document

... that strong convergence is guaranteed that has recently been ...CQ method and proved the following strong convergence theorem for a nonexpansive mapping T in a Hilbert space ... See full document

... an equilibrium problem based on a projection algorithm in a nonuniformly smooth Banach ...a projection algorithm is introduced and the convergence analysis is ...A strong ... See full document

... the equilibrium problem and fixed point prob- lems of strict pseudo-contraction mappings T by an iterative scheme for finding an ele- ment of EP(F) ∩ F(T ...iterative method Liu [] pro- posed the ... See full document

... extragradient method for fixed point problems and variational inequality problems,” Journal of Inequalities and Applications, ...“Strong convergence theorems for a generalized ... See full document

... the gradient projection algorithm and the hybrid steepest descent method and prove the strong convergence to a common element of the equilibrium problem; the null ... See full document

... in the setting of Hilbert spaces or uniformly convex Banach spaces. Although nonexpansive mappings are 0-strict pseudocontractions, iterative methods for k-strict pseudocontractions are far less developed than ... See full document

... the generalized equilibrium problem ...shrinking projection algorithm which was first introduced by Takahashi et ...A strong convergence of common elements of the fixed point ... See full document