[PDF] Top 20 Strong convergence and control condition of modified Halpern iterations in Banach spaces

... smooth Banach space has a uniformly Gˆateaux differentiable norm and is such that every nonempty closed convex and bounded subset of X has the fixed point property for nonexpansive ...real Banach ... See full document

... Hilbert spaces to real Banach spaces with uniformly Gâteaux differentiable norms and in which each nonempty, closed, convex and bounded subset has the fixed point property for nonexpansive ...another ... See full document

... smooth Banach space. In the meantime, we remove the control condition (C) and replace condition (C) with (C ) (defined below) in the result of Tian ... See full document

... There are number of papers dealing with the approximation of fixed points / common fixed points of asymptotically nonexpansive and asymptotically quasi- nonexpansive mappings in uniformly convex Banach ... See full document

... of Banach spaces and proved that if E is a uniformly smooth Banach space, then x t converges strongly to a fixed point of T and the limit defines the (unique) sunny nonexpansive retraction from C ... See full document

... two modified Mann iterations for nonexpansive semigroups {T(t) : 0 ≤ t < ∞ } and obtained the strong convergence theorems in a reflexive Banach space E which admits a weakly ... See full document

... We consider the problem of the convergence of the three-steps iterative sequences for asymptotically nonexpansive mappings in a real Banach space. Under suitable conditions, it has been proved that the ... See full document

... modified Halpern iteration for a countable family of Bregman totally quasi-asymptotically nonexpansive multi-valued mappings in the framework of reflexive Banach spaces, and to prove strong ... See full document

... real Banach spaces with a norm-to-norm uniformly continuous duality selection ...the convergence proof of Halpern iterations by Shioji and Takahashi [] for the extraction of rates of ... See full document

... T . However, even in a Hilbert space, the Mann iteration may fail to converge strongly []. Some attempts to construct an iteration method guaranteeing the strong convergence have been made. For example, ... See full document

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

... some strong convergence theorems for fixed points of modified Ishikawa and Halpern iterative processes for a countable family of hemi-relatively nonexpansive mappings in a uniformly convex and ... See full document

... Pre-Hilbert spaces see 14, R-trees see 15, Euclidean buildings see 16, the complex Hilbert ball with a hyperbolic metric see 17, and many ...these spaces and of the fundamental role they play in geometry, ... 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

... between convergence of two kinds of the iterative ...Ishikawa) iterations (with errors) converge strongly to fixed points of pseudocontractive mappings and others under appropriate ... See full document

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

... demicompact at 0 (e.g., see [21]). T is said to be demicompact on C if T is demicompact for each y ∈ C. If T is compact on C, then T is demicompact on C. For examples of demicompact mappings, see [1, 2, 12, 13]. We also ... See full document

... Theorem 4.1 Let C be a nonempty closed convex subset of a uniformly convex and 2-uniformly smooth Banach space E which admits a weakly sequentially continuous duality mapping. Let Q be a sunny nonexpansive ... See full document

... Let E be a real Banach space. A subset C of E is called a retract of E if there exists a continuous mapping P : E → K such that Px = x for all x ∈ C. Every closed convex subset of a uniformly convex Banach ... See full document

... Recently, Zhou [1] extended Schu’s results by establishing a fixed point theorem for asymptotically pseudo-contraction without any compact assumption on the mappings. By modifying the algorithm used in Theorem 1.2, Schu ... See full document