scholarly journals Convergence theorems for strict pseudo-contractions in CAT(0) metric spaces

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 1967-1971
Author(s):  
Amir Gharajelo ◽  
Hossein Dehghan
Keyword(s):  
Strong Convergence ◽  
Iterative Algorithm ◽  
Metric Spaces ◽  
Convergence Theorems ◽  
Demiclosed Principle ◽  
Contractive Mappings

In this paper, we introduce the notion of strict pseudo-contractive mappings in the framework of CAT(0) metric spaces. Some properties of such mappings including demiclosed principle are investigated. Also, strong convergence and ?-convergence of the well-known Mann iterative algorithm is established for strict pseudo-contractive mappings.

scholarly journals Approximation of viscosity zero points of accretive operators in a Banach space

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2175-2184
Author(s):  
Sun Cho ◽  
Shin Kang
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Iterative Algorithm ◽  
Accretive Operators ◽  
Convergence Theorems ◽  
Computational Errors ◽  
Zero Points

In this paper, zero points of m-accretive operators are investigated based on a viscosity iterative algorithm with double computational errors. Strong convergence theorems for zero points of m-accretive operators are established in a Banach space.

scholarly journals Approximation of Fixed Points of C*-Algebra-Multi-Valued Contractive Mappings by the Mann and Ishikawa Processes in Convex C*-Algebra-Valued Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 392
Author(s):  
Azadeh Ghanifard ◽  
Hashem Parvaneh Masiha ◽  
Manuel De La Sen
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Infinite Family ◽  
Convergence Theorems ◽  
Ishikawa Iteration ◽  
C Algebra ◽  
Contractive Mappings

The aim of the present paper is to state and prove some convergence theorems for the Mann and Ishikawa iteration schemes involving C * -algebra-multi-valued contractive mappings in the setting of convex C * -algebra-valued metric spaces. The convergence theorems of the proposed iterations to a common fixed point of finite and infinite family of such mappings are also established.

Iterative Methods for Strictly Pseudo-Contractive Mappings

2013 ◽  
Vol 333-335 ◽  
pp. 1402-1405
Author(s):  
Yang Liu ◽  
Yan Hao
Keyword(s):  
Banach Space ◽  
Iterative Method ◽  
Strong Convergence ◽  
Iterative Methods ◽  
Smooth Banach Space ◽  
Convergence Theorems ◽  
Uniformly Smooth Banach Space ◽  
Contractive Mappings ◽  
Uniformly Smooth

The aim of this work is to consider an iterative method for a-strict pseudo-contractions. Strong convergence theorems are established in a real 2-uniformly smooth Banach space.

scholarly journals Iterative Algorithm andΔ-Convergence Theorems for Total Asymptotically Nonexpansive Mappings in CAT(0) Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
J. F. Tang ◽  
S. S. Chang ◽  
H. W. Joseph Lee ◽  
C. K. Chan
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Algorithm ◽  
Convergence Theorem ◽  
Nonexpansive Mappings ◽  
Convergence Theorems ◽  
Demiclosed Principle ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Total Asymptotically Nonexpansive Mappings

The main purpose of this paper is first to introduce the concept of total asymptotically nonexpansive mappings and to prove aΔ-convergence theorem for finding a common fixed point of the total asymptotically nonexpansive mappings and the asymptotically nonexpansive mappings. The demiclosed principle for this kind of mappings in CAT(0) space is also proved in the paper. Our results extend and improve many results in the literature.

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