Convergence of three-step iterations for Ciric-quasi contractive operator in CAT(0) spaces

Abstract In this paper, we study three-step iteration process for Ciric-quasi contractive operator and establish strong convergence theorems for above mentioned operator and schemes in the setting of CAT(0) spaces. Our result extends and generalizes some previous work from the existing literature (see, e.g., [4, 30] and some others).

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Weak and strong convergence theorems of three step iteration process with errors for nonself-asymptotically nonexpansive mappings

Mathematical and Computer Modelling ◽

10.1016/j.mcm.2010.05.006 ◽

2010 ◽

Vol 52 (5-6) ◽

pp. 772-780 ◽

Cited By ~ 6

Author(s):

Liping Yang ◽

Xiangsheng Xie

Keyword(s):

Strong Convergence ◽

Nonexpansive Mappings ◽

Iteration Process ◽

Weak And Strong Convergence ◽

Convergence Theorems ◽

Asymptotically Nonexpansive Mappings ◽

Asymptotically Nonexpansive

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Approximating the zeros of accretive operators by the Ishikawa iteration process

Abstract and Applied Analysis ◽

10.1155/s1085337596000073 ◽

1996 ◽

Vol 1 (2) ◽

pp. 153-167 ◽

Cited By ~ 15

Author(s):

Zhou Haiyun ◽

Jia Yuting

Keyword(s):

Strong Convergence ◽

Banach Spaces ◽

Iteration Process ◽

Accretive Operators ◽

Convergence Theorems ◽

Ishikawa Iteration ◽

Uniformly Smooth ◽

Ishikawa Iteration Process ◽

Uniformly Smooth Banach Spaces ◽

Iteration Processes

Some strong convergence theorems are established for the Ishikawa iteration processes for accretive operators in uniformly smooth Banach spaces.

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Hybrid Implicit Iteration Process for a Finite Family of Non-Self-Nonexpansive Mappings in Uniformly Convex Banach Spaces

Journal of Applied Mathematics ◽

10.1155/2014/238053 ◽

2014 ◽

Vol 2014 ◽

pp. 1-5

Author(s):

Qiaohong Jiang ◽

Jinghai Wang ◽

Jianhua Huang

Keyword(s):

Strong Convergence ◽

Banach Spaces ◽

Nonexpansive Mappings ◽

Iteration Process ◽

Finite Family ◽

Uniformly Convex ◽

Weak And Strong Convergence ◽

Convergence Theorems ◽

Uniformly Convex Banach Spaces ◽

Implicit Iteration

Weak and strong convergence theorems are established for hybrid implicit iteration for a finite family of non-self-nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper extend and improve some recent results.

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STRONG CONVERGENCE THEOREMS OF ISHIKAWA ITERATION PROCESS WITH ERRORS FOR FIXED POINTS OF LIPSCHITZ CONTINUOUS MAPPINGS IN BANACH SPACES

Taiwanese Journal of Mathematics ◽

10.11650/twjm/1500403842 ◽

2006 ◽

Vol 10 (2) ◽

pp. 543-552 ◽

Cited By ~ 8

Author(s):

Yen-Cherng Lin ◽

Ngai-Ching Wong ◽

Jen-Chih Yao

Keyword(s):

Strong Convergence ◽

Fixed Points ◽

Banach Spaces ◽

Iteration Process ◽

Convergence Theorems ◽

Ishikawa Iteration ◽

Lipschitz Continuous ◽

Continuous Mappings ◽

Ishikawa Iteration Process

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Convergence Theorems on a New Iteration Process for Two Asymptotically Nonexpansive Nonself-Mappings with Errors in Banach Spaces

Discrete Dynamics in Nature and Society ◽

10.1155/2010/307245 ◽

2010 ◽

Vol 2010 ◽

pp. 1-19

Author(s):

Murat Ozdemir ◽

Sezgin Akbulut ◽

Hukmi Kiziltunc

Keyword(s):

Banach Space ◽

Strong Convergence ◽

Iterative Scheme ◽

Iteration Process ◽

Convex Banach Space ◽

Uniformly Convex Banach Space ◽

Uniformly Convex ◽

Weak And Strong Convergence ◽

Convergence Theorems ◽

Asymptotically Nonexpansive

We introduce a new two-step iterative scheme for two asymptotically nonexpansive nonself-mappings in a uniformly convex Banach space. Weak and strong convergence theorems are established for this iterative scheme in a uniformly convex Banach space. The results presented extend and improve the corresponding results of Chidume et al. (2003), Wang (2006), Shahzad (2005), and Thianwan (2008).

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Weak and Strong Convergence Theorems of an Implicit Iteration Process for a Countable Family of Nonexpansive Mappings

Fixed Point Theory and Applications ◽

10.1155/2008/732193 ◽

2008 ◽

Vol 2008 (1) ◽

pp. 732193 ◽

Cited By ~ 1

Author(s):

Kittikorn Nakprasit ◽

Weerayuth Nilsrakoo ◽

Satit Saejung

Keyword(s):

Strong Convergence ◽

Nonexpansive Mappings ◽

Iteration Process ◽

Countable Family ◽

Weak And Strong Convergence ◽

Convergence Theorems ◽

Implicit Iteration Process ◽

Implicit Iteration

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Convergence theorems for generalized hemicontractive mapping in p-uniformly convex metric space

Journal of Applied Analysis ◽

10.1515/jaa-2020-2017 ◽

2020 ◽

Vol 26 (2) ◽

pp. 221-229

Author(s):

Godwin C. Ugwunnadi ◽

Chinedu Izuchukwu ◽

Oluwatosin T. Mewomo

Keyword(s):

Fixed Point ◽

Strong Convergence ◽

Metric Spaces ◽

Iteration Process ◽

Uniformly Convex ◽

Convex Metric Space ◽

Convergence Theorems ◽

Uniformly Convex Metric Space ◽

Convex Metric Spaces ◽

Hemicontractive Mappings

AbstractIn this paper, we introduce and study an Ishikawa-type iteration process for the class of generalized hemicontractive mappings in 𝑝-uniformly convex metric spaces, and prove both Δ-convergence and strong convergence theorems for approximating a fixed point of generalized hemicontractive mapping in complete 𝑝-uniformly convex metric spaces. We give a surprising example of this class of mapping that is not a hemicontractive mapping. Our results complement, extend and generalize numerous other recent results in CAT(0) spaces.

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Convergence theorems for a family of multivalued nonexpansive mappings in hyperbolic spaces

Open Mathematics ◽

10.1515/math-2016-0095 ◽

2016 ◽

Vol 14 (1) ◽

pp. 1065-1073 ◽

Cited By ~ 1

Author(s):

Osman Alagoz ◽

Birol Gunduz ◽

Sezgin Akbulut

Keyword(s):

Strong Convergence ◽

Nonexpansive Mappings ◽

Iteration Process ◽

Finite Family ◽

Hyperbolic Spaces ◽

Multivalued Mappings ◽

Convergence Theorems

AbstractIn this article we modify an iteration process to prove strong convergence and Δ— convergence theorems for a finite family of nonexpansive multivalued mappings in hyperbolic spaces. The results presented here extend some existing results in the literature.

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