Mann’s algorithm for nonexpansive mappings in CAT() spaces

He, Jin-Su; Fang, Dingzhi; López-Acedo, Genaro; Li, C.

doi:10.1016/j.na.2011.07.070

Cited by 41 publications

(27 citation statements)

References 12 publications

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“…The results of a CAT(0) space can be applied to any CAT(κ) space with κ ≤ 0 since any CAT(κ) space is a CAT(κ ) space for every κ ≥ κ (see in [5]). Although, CAT(κ) spaces for κ > 0, were studied by some authors (see e.g., [13,15,25]). …”

Section: Introductionmentioning

confidence: 99%

On strong and Δ -convergence of modified S-iteration for uniformly continuous total asymptotically nonexpansive mappings in CAT(κ) spaces

Saipara¹,

Chaipunya²,

Cho³

2015

J. Nonlinear Sci. Appl.

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Section: Introductionmentioning

confidence: 99%

On strong and Δ -convergence of modified S-iteration for uniformly continuous total asymptotically nonexpansive mappings in CAT(κ) spaces

Saipara¹,

Chaipunya²,

Cho³

2015

J. Nonlinear Sci. Appl.

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“…Lemma (He et al) Let ( X , ρ ) be a complete CAT(1) space and let p ∈ X . Suppose that the sequence { x n } in X Δ‐converges to x such that

r false(p, false{x_{n} false} false) < \frac{D_{κ}}{2}

.…”

Section: Preliminariesmentioning

confidence: 85%

“…Lemma (He et al) Let ( X , ρ ) be a complete CAT(1) space and let K be a nonempty subset of X . Suppose that the sequence { x n } in X is Fejer monotone with respect to K and the asymptotic radius r ({ x n }) of { x n } is less than

\frac{π}{2}

.…”

Section: Preliminariesmentioning

confidence: 99%

“…In 2012, He et al used iterative method for approximating fixed points in CAT( κ ) spaces and proved some convergence theorems under standard mild conditions, in which the sequence { x n } is generated by

x_{n + 1} = a_{n} T x_{n} \oplus false(1 - a_{n} false) x_{n},

for all n ≥ 0, where sequence { a n } is in (0,1).…”

Section: Introductionmentioning

confidence: 99%

“…For CAT(κ) spaces with κ>0 were studied by some researchers. [24][25][26][27] Furthermore, many researchers studied and introduced various iteration processes for approximating fixed points in the framework of CAT(κ) spaces.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Convergence analysis of modified iterative approaches in geodesic spaces with curvature bounded above

Thounthong

Pakkaranang

Saipara

et al. 2019

Math Methods in App Sciences

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The objective of this article is to establish a new modified iteration process for nonexpansive mappings in complete CAT(κ) spaces. We prove strong and Δ‐convergence theorems of the proposed method in such spaces under some standard conditions. Furthermore, numerical experiments of non‐trivial examples are also provided to show performance and comparison speed of convergence with many previously known methods. Our main result extended and improved the corresponding recent results announced by many researchers.

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On modified proximal point algorithms for solving minimization problems and fixed point problems in CAT(κ) spaces

Pakkaranang

Wen

Yao

et al. 2019

Math Methods in App Sciences

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In this paper, we show the existence of solutions of the convex minimization problems and common fixed problems in CAT(1) spaces under some mild conditions. For this, we propose the new modified the proximal point algorithm.Further, we give some applications for the convex minimization problem and the fixed point problem in CAT(𝜅) spaces with the bounded positive real number 𝜅. Our results improve and generalize many recent important results in the literature.

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Mann’s algorithm for nonexpansive mappings in CAT() spaces

Cited by 41 publications

References 12 publications

On strong and Δ -convergence of modified S-iteration for uniformly continuous total asymptotically nonexpansive mappings in CAT(κ) spaces

On strong and Δ -convergence of modified S-iteration for uniformly continuous total asymptotically nonexpansive mappings in CAT(κ) spaces

Convergence analysis of modified iterative approaches in geodesic spaces with curvature bounded above

On modified proximal point algorithms for solving minimization problems and fixed point problems in CAT(κ) spaces

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