[PDF] Top 20 A new composite implicit iterative process for a finite family of nonexpansive mappings in Banach spaces

... In order to prove the main results of this paper, we need the following lemmas. Lemma 1.2 [2]. Let E be a uniformly convex Banach space, let K be a nonempty closed convex subset of E, and let T : K → K be a ... See full document

... a finite family of relatively nonexpansive mappings in Banach ...convex Banach space E, then the generalized projection Π C (see, Alber [15] or Kamimura and ... See full document

... a Banach space E such that C is nonempty closed convex and D ⊂ C, then a map Q : C → D is sunny see 12, 13 provided Qx tx − Qx Qx for all x ∈ C and t ≥ 0 whenever x tx − Qx ∈ ...sunny nonexpansive ... See full document

... an η-strongly monotone and k-Lipschitzian mapping, μ is a positive fixed constant. In the same year, Osilike et al. [] extended the results of Wang from Hilbert spaces to arbitrary Banach spaces and ... See full document

... points iterative technique for (self or nonself) asymptotically nonexpansive mappings in Banach spaces, including Mann type iteration, Ishikawa type iteration, and three-step type ... See full document

... an implicit iterative process with errors converges weakly and strongly to a common fixed point of a finite family of asymptotically quasi-nonexpansive mappings on ... See full document

... this iterative scheme converges weakly or strongly to a common fixed point of a finite family of asymptotically nonexpansive mappings in uniformly convex Banach ... See full document

... onto C is not generally nonexpansive. Our purpose in the present paper is to obtain an analogous result for a finite family of relatively nonexpansive mappings in Banach ... See full document

... a finite family of nonexpansive mappings has been considered by many authors see 1–4 and the references ...a family of nonexpansive mappings see 5, ...a family of ... See full document

... pseudocontractive mappings has been studied by several au- thors (see [, –] and the references cited therein) by using the modified Mann iteration process (see []) and the modified Ishikawa iteration ... See full document

... a Banach space and Shioji and Takahashi [19] im- proved Wittmann’s result to a certain Banach ...above iterative scheme with the necessary conditions on the parameters and some additional conditions ... See full document

... a new implicit iteration process with errors for finite families of strictly asymptot- ically pseudocontractive mappings and nonexpansive mappings is ...the ... See full document

... ) spaces are uniquely geodesic ...CAT(κ) spaces with κ ≥ . Since most of the results for such spaces are easily deduced from those for CAT() spaces, in what follows, we mainly focus on ... See full document

... one-parameter nonexpansive semigroup in a Banach space under some appropriate control ...the iterative scheme which solve some variational ...a new composite explicit viscosity ... See full document

... A metric space X, d is said to be a length space if any two points of X are joined by a rectifiable path i.e., a path of finite length, and the distance between any two points of X is taken to be the infimum of ... See full document

... Throughout this paper, we assume that E and E ∗ is a real Banach space and the dual space of E, respectively. Let T be a mapping from C into itself, where C is a subset of E. We denoted by F(T) the set of fixed ... See full document

... iteration process is defined. If one assumes that the iteration process is always defined, our result will hold for even the more general class of asymptotically hemicontractive maps ...(i.e., ... See full document

... the iterative approximation of fixed points of asymptotically nonexpansive mappings, asymptotically quasi-nonexpansive mappings, asymptoti- cally nonexpansive mappings in ... See full document

... from nonexpansive mapping to nonexpansive semigroup, and from contractive mapping to φ-strongly pseudocontractive mapping and pseudocontractive mapping, ... See full document

... Iteration (3.1) has been considered in [2, 6, 7, 11, 12]. Iteration (3.1) has been dis- cussed in [1, 10]. Note that iteration (1.2) is a particular case of (3.1). However, as far as we know, no such paper is dedicated ... See full document