[PDF] Top 20 Convergence theorems for some multi-valued generalized nonexpansive mappings

... for multi-valued contractions and nonexpansive mappings us- ing the Hausdorff metric was initiated by Markin [] and Nadler ...of multi-valued mappings has been rapidly ... See full document

... of generalized nonexpansive mappings on star-shaped sets and establish strong convergence theorems of the Halpern iterative sequences generated by these mappings in a real ... See full document

... of generalized asymptotically nonexpansive mapping and gave a necessary and sufficient condition for the modi- fied Ishikawa and Mann iterative sequences to converge to fixed points for the class of ...the ... See full document

... existence theorems of fixed points were established; see, for example, ...nonlinear mappings, but also to be able to construct an iterative process to approximate their fixed ... See full document

... “Strong convergence theorems for a generalized equilibrium problem with a relaxed monotone mapping and a countable family of nonexpansive mappings in a Hilbert space,” Fixed Point ... See full document

... free nonexpansive mppings on, even weakly compact, subsets of uniformly convex Banach ...single valued mappings, nonexpansive mappings is guaranteed(see ... See full document

... where dist(x, D) = inf { x – y : y ∈ D } is the distance from a point x to a subset D. Let t be a single-valued mapping of D into D and T be a multi-valued mapping of D into CB(D). The set of fixed ... See full document

... improved some important theorems such as Caristi’s fixed point theorem, Ekeland’s variational principle and the nonconvex minimization ...proved some results on fixed point problems and also showed ... 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

... strong convergence (norm convergence) is often much more desirable than weak convergence, for it translates the physical- ly tangible property that the energy kx n −xk of the error between the ... See full document

... Throughout this article, we denote by N and ℝ the sets of positive integers and real numbers, respectively. Let D be a nonempty closed subset of a real Banach space E. A single-valued mapping T : D ® D is called ... See full document

... strong convergence and ∆-convergence theorems for the class of generalized non-expansive multi-valued maps in a CAT(0) ...improves some recent results announced in the ... See full document

... equality generalized mixed equilibrium problem, which is more general than many problems such as split feasibility problem, split equality problem, split equilibrium problem, and so ...weak convergence ... See full document

... As we all know that if C is a nonempty closed convex subset of a Hilbert space H and P C : H → C is the metric projection of H onto C, then P C is nonexpansive. This fact actually characterizes Hilbert spaces and ... See full document

... The remainder of the proof is the same as Theorem . of []. Theorem . Let E be a uniformly convex Banach space with a uniformly Gâteaux differ- entiable norm, K be a nonempty, closed, and convex subset of E, T : K → ... See full document

... for nonexpansive mappings have been introduced (see [–]); furthermore, many strong convergence theorems for nonexpansive mappings have been ...nonlinear mappings which ... See full document

... Let D be a nonempty closed convex subset of a real Banach space X. A single-valued mapping T : D ® D is called nonexpansive if ||T(x) - T(y)|| ≤ ||x - y|| for all x, y Î D. Let N(D) and CB(D) denote the ... See full document

... prove some weak and strong convergence theorems of the iterative scheme () in CAT() spaces for generalized nonexpansive mappings enabling us to enlarge the class of underlying ... See full document

... for multi-valued mappings in Banach ...proved some con- vergence theorems for multi-valued mappings in uniformly convex Banach ... See full document

... convergence theorem in a real uniformly smooth and strictly convex Banach space with Kadec-Klee property. In order to get the theorems, the hybrid algorithms are presented and are used to approximate the ... See full document