[PDF] Top 20 Convergence theorems of modified Mann iterations
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Convergence theorems of modified Mann iterations
... modified Mann itera- tion processes for nonexpansive mappings, asymptotically nonexpansive mappings T and nonexpansive semigroups, asymptotically nonexpansive semigroups S = {T (t) : t ≥ }, re- spectively, with C ... See full document
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Strong Convergence Theorems for Strict Pseudocontractions in Uniformly Convex Banach Spaces
... strong convergence theorems of the modified Mann iteration scheme to λ -strict pseudocontractions in p -uniformly convex Banach spaces with a uniformly Gˆateaux differentiable ... See full document
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Strong Convergence of Modified Halpern Iterations in CAT(0) Spaces
... Fixed point theory in CAT0 spaces was first studied by Kirk see 18, 19. He showed that every nonexpansive single-valued mapping defined on a bounded closed convex subset of a complete CAT0 space always has a fixed point. ... See full document
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Strong Convergence Theorems of Modified Ishikawa Iterations for Countable Hemi-Relatively Nonexpansive Mappings in a Banach Space
... the Mann iteration process to modify Ishikawa iteration process and from countable relatively nonexpansive mappings to more general countable hemi- relatively nonexpansive mappings; that is, we relax the strong ... See full document
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Strong convergence theorems for modifying Halpern-Mann iterations for a quasi-ϕ-asymptotically nonexpansive multi-valued mapping in Banach spaces
... The purpose of this paper is to introduce modifying Halpern-Mann’s iterations sequence for a quasi- φ -asymptotically nonexpansive multi-valued mapping. Under suitable limit conditions, some strong ... See full document
12
The equivalence between the convergence of the modified Mann and Ishikawa iterations for asymptotically pseudocontractive mappings obtained by dropping the bounded assumption
... The aim of this paper is to revise the results of the papers [, , ] and remove the as- sumption T with bounded range []. We obtain that the modified Ishikawa iteration with errors converges strongly to the fixed point ... See full document
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Strong convergence theorems for uniformly L Lipschitzian asymptotically pseudocontractive mappings in Banach spaces
... strong convergence theorems of the modified Ishikawa and Mann iterations with errors of uniformly L-Lipschitzian asymptotically pseudocontractive mappings in real Banach ... See full document
11
The convergence of the modified Mann and Ishikawa iterations in Banach spaces
... nontrivial Mann iteration failing to converge while Ishikawa iteration ...between convergence of two kinds of the iterative ...the Mann (modified Mann) and Ishikawa (modified Ishikawa) ... See full document
12
Strong convergence theorems by Halpern Mann iterations for multi valued relatively nonexpansive mappings in Banach spaces with applications
... e., J is continuous from the strong topology of E to the weak star topology of E*; iv If E is a uniformly smooth Banach space, then J is uniformly continuous on each bounded subset of E;[r] ... See full document
10
Strong convergence and control condition of modified Halpern iterations in Banach spaces
... Remark 3.3. We note that every uniformly 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 ... See full document
10
Convergence and summable almost T stability of the random Picard Mann hybrid iterative process
... They also established the Bochner integrability of random fixed point for such random operators. Beg et al. [] recently studied the almost sure T -stability and strong conver- gence of the random Halpern iteration ... See full document
14
The convergence of implicit Mann and Ishikawa iterations for weak generalized φ hemicontractive mappings in real Banach spaces
... Let E be a real Banach space and let D be a nonempty closed convex subset of E, let T : D → D be a continuous weak generalized ϕ -hemicontractive mapping. The existence theorem of a fixed point of a weak generalized ϕ ... See full document
11
The equivalence of Mann iteration and Ishikawa iteration for non Lipschitzian operators
... Theorem 2.3 [10] . Let K be a closed convex (not necessary bounded) subset of an arbitrary Banach space X and let T be a Lipschitzian pseudocontrac- tive selfmap of K . We consider Mann iteration and Ishikawa ... See full document
7
On Multistep Iterative Scheme for Approximating the Common Fixed Points of Contractive Like Operators
... We introduce the Jungck-multistep iteration and show that it converges strongly to the unique common fixed point of a pair of weakly compatible generalized contractive-like operators defined on a Banach space. As ... See full document
11
Strong convergence of modified Halpern’s iterations for a k strictly pseudocontractive mapping
... We will show that the sequence {αn } satisfying the conditions C and C is sufficient to guarantee the strong convergence of the modified Halpern’s iterative sequences .-. for k-strict[r] ... See full document
10
Nonexpansive semigroups in CAT(κ) spaces
... This paper is organized as follows. In Section we recall the definition of geodesic met- ric spaces and summarize some useful lemmas and the main properties of CAT(κ) spaces. In Section we present some technical ... See full document
17
Halpern's Iteration in CAT(0) Spaces
... weak convergence in Banach space setting. Several convergence theorems for finding a fixed point of a nonexpansive mapping have been established with respect to this type of convergence ... See full document
13
Demiclosed Principle for Asymptotically Nonexpansive Mappings in CAT(0) Spaces
... We prove the demiclosed principle for asymptotically nonexpansive mappings in CAT0 spaces. As a consequence, we obtain a Δ-convergence theorem of the Krasnosel’skii-Mann iteration for asymptotically ... See full document
14
The Equivalence between -Stabilities of The Krasnoselskij and The Mann Iterations
... where λ ∈ (0, 1). Recently, the equivalence between the T-stabilities of Mann and Ishikawa iterations, respectively, for modified Mann-Ishikawa iterations was shown in [5]. In the ... See full document
7
Approximating Fixed Points of Nonexpansive Nonself Mappings in CAT(0) Spaces
... Kaewkhao, “Common fixed points of a nonexpansive semigroup and a convergence theorem for Mann iterations in geodesic metric spaces,” Nonlinear Analysis: Theory, Methods & Application[r] ... See full document
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