[PDF] Top 20 Strong convergence theorems for modifying Halpern iterations for a totally quasi ϕ asymptotically nonexpansive multi valued mapping in reflexive Banach spaces

... Throughout this paper, we denote by N and R the sets of positive integers and real num- bers, respectively. Let D be a nonempty closed subset of a real Banach space X. A mapping T : D → D is said to be ... See full document

... and strong convergence of iterative sequences to approximate a common element of the set of solutions for a generalized MEP, the set of solutions for variational inequality problems, and the set of common ... See full document

... convex Banach space with Kadec-Klee property, and C be a nonempty closed and convex subset of ...total quasi- ϕ -asymptotically nonexpansive multi-valued mapping ... See full document

... a reflexive, strictly convex, and smooth Banach ...duality mapping J* from E* onto E** = E coincides with the inverse of the duality mapping J from E onto E*, that is, J* = J -1 ...following ... See full document

... firmly nonexpansive single value mappings was studied in ...and totally convex on bounded subsets of X, then F(T) = F(T) and ˆ F(T ) is closed and convex (see ...firmly nonexpansive mapping is ... See full document

... where the initial guess x 1  D is arbitrary and    n is a real sequence in   0 1  . It is known that under appro- priate settings the sequence  x n  converges weakly to a fixed point of T . However, even in a ... See full document

... of totally quasi- φ -asymptotically nonexpansive multi-valued ...A strong convergence theorem for solving generalized mixed equilibrium problems is established in ... See full document

... exists, where S(x) = {x : x = ,x ∈ X}. In this case, X is said to be smooth. The norm of Banach space X is said to be Fréchet differentiable, if, for each x ∈ S(x), the limit (.) is attained uniformly for y ∈ ... See full document

... introduce modifying Halpern-Mann’s iterations sequence for a quasi- φ -asymptotically nonexpansive multi-valued ...some strong convergence ... See full document

... reflexive Banach space, let D be a nonempty, closed, and convex subset of X and let G : D × D → R be a bifunction satisfying the con- ditions: (A) G(x, x) = , for all x ∈ D; (A) G(x, y) + G(y, x) ≤ , for any x, ... See full document

... consider strong convergence results for Bregman strongly nonexpansive mappings in reflexive Banach spaces by modifying Halpern and Mann’s iter- ...strongly ... See full document

... prove strong convergence theorems to a point which is a fixed point of multi-valued mappings, a zero of an α -inverse-strongly monotone operator and a solution of the equilibrium ... See full document

... of nonexpansive mappings is an important subject in the theory of nonexpansive mappings and its applications in a number of applied areas, in particular, in image recovery and signal processing (see [1, 2, ... See full document

... let ϕ = {T (s) : s ∈ S} be an asymp- totically nonexpansive semigroup on a nonempty compact convex subset C of a smooth Banach space E such that Fix(ϕ) = ∅ ...contractive mapping of the ... 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 ... See full document

... total quasi-j-asymptotically nonexpansive mappings and null spaces of finite family of g-inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach ... See full document

... relaxed Halpern-type iterative algorithm for approximating some common fixed point of a kind of nonlinear mappings and obtain a strong convergence theorem under suitable ...uniformly totally ... See full document

... the multi-step iterative algorithm with bounded errors ...generalized asymptotically quasi-nonexpansive map- pings to converge to common fixed points in Banach ... See full document

... smooth Banach space such that E has the Kadec-Klee ...η-α-monotone mapping, let be a bi- function from C × C to R satisfying (C)-(C), and let f be a proper convex and lower semicontinuous function from C ... See full document

... Inspired and motivated by this facts, we define and study the convergence theorems of two steps iterative sequences for total asymptotically nonexpansive nonself-mappings in Banach ... See full document