[PDF] Top 20 Convergence theorems for common solutions of various problems with nonlinear mapping

... Equilibrium problems, which were introduced in [] in , have had great impact and influence on the development of several branches of pure and applied ...numerous problems in economics, finance, physics, ... See full document

... of nonlinear mappings has been stud- ied extensively by many authors to solve nonlinear mapping equations as well as varia- tional inequality problems and their generalizations (see, ...of ... See full document

... Equilibrium problems which were introduced by Blum and Oettli [] have intensively been ...equilibrium problems cover fixed point problems, varia- tional inequality problems, inclusion ... See full document

... It is well known that if X ∗ is strictly convex, then J is single-valued. In the sequel, we shall still denote the single-valued normalized duality mapping by J. Let C be a nonempty closed convex subset of X, f : ... See full document

... of problems which arise in economics, finance, image reconstruction, ecology, transporta- tion, network, elasticity and optimization; see [–] and the references ...of solutions is important in the study ... See full document

... a common element of the fixed points set of relatively nonexpansive mapping, the solution set of equili- brium problem and solution set of variational inequality problem for g-inverse mono- tone ... See full document

... the problems of finding a common element in the set of solution of variational inequalities for an inverse-strongly monotone mapping and in the set of fixed points of nonexpansive mappings or strict ... See full document

... inverse problems which arise from phase retrievals and in medical image reconstruction ...in various disciplines such as image restoration, computer to- mography and radiation therapy treatment planning ... See full document

... monotone mapping, solutions of a monotone variational inequality, and fixed points of a strict pseudocontraction are ...the convergence of the iterative sequences. Strong convergence ... See full document

... weak convergence theorems for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a relatively nonexpansive mapping in Banach ... See full document

... strong convergence theorems for finding a common element of the set of solutions of a finite family of split equilibrium problems and the set of common fixed points of a countable ... See full document

... monotone mapping T : H → 2 H is said to be maximal if the graph of G(T ) of T is not properly contained in the graph of any other monotone ...set-valued mapping T : H → 2 H is said to be monotone if, for ... See full document

... a common solution problem is investigated based on a projection ...Strong convergence theorems for common solutions of a system of equilibrium problems and a family of ... See full document

... a common element of the set of solutions of a mixed equilibrium problem for an equilibrium bifunction, the set of fixed points of an infinite family of nonexpansive mappings, the set of solutions of ... See full document

... Corollary 2.2. Let C be a nonempty closed convex subset of a real Hilbert space H. Let F be a bifunction from C × C to R which satisfies (A1)–(A4). Let A : C → H be an α-inverse-strongly monotone mapping, T : C → ... See full document

... It follows from Theorem 2.1 and the above two conclusions that T is a weak relatively nonexpansive mapping but not relatively nonexpansive mapping. We have also the following conclusions: 1 T is not ... See full document

... proposed the viscosity approximation method of selecting a particular fixed point of a given non-expansive mapping in Hilbert spaces. If H is a Hilbert space, T : C → C is a non- expansive self-mapping on a ... See full document

... Zembayashi, “Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications [r] ... See full document

... In this section, we prove strong convergence of an iterative sequence generated by the hybrid method in mathematical programming. We start with the following useful common tools. Lemma 3.1. Let C be a ... See full document

... In , Osilike [] introduced a class of nonspreading type mappings, which is more general than the mappings studied in [] in Hilbert spaces, and proved some weak and strong convergence theorems in ... See full document