scholarly journals The Convergence of Three-Step Iterative Schemes for Generalized Φ − Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Linxin Li ◽  
Dingping Wu
Keyword(s):  
Banach Space ◽  
Fixed Points ◽  
Rate Of Convergence ◽  
Iterative Process ◽  
Smooth Banach Space ◽  
Iterative Schemes ◽  
Uniformly Smooth Banach Space ◽  
Contractive Mappings ◽  
Uniformly Smooth ◽  
Accretive Mappings

Charles proved the convergence of Picard-type iteration for generalized Φ − accretive nonself-mappings in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly Φ − quasi-accretive mappings and fixed points of strongly Φ − hemi-contractions, we extend the results to Noor iterative process and SP iterative process for generalized Φ − hemi-contractive mappings. Finally, we analyze the rate of convergence of four iterative schemes, namely, Noor iteration, iteration of Corollary 2, SP iteration, and iteration of Corollary 4.

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 The Convergence of Mann Iteration for Generalized Φ- hemi-contractive Maps

2020 ◽  
pp. 39-52
Author(s):  
Linxin Li ◽  
Dingping Wu
Keyword(s):  
Banach Space ◽  
Fixed Points ◽  
Iteration Process ◽  
Smooth Banach Space ◽  
Mann Iteration ◽  
Uniformly Smooth Banach Space ◽  
Uniformly Smooth ◽  
Contractive Maps ◽  
Mann Iteration Process

Abstract Charles[1] proved the convergence of Picard-type iterative for generalized Φ− accretive non-self maps in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly Φ − accretive and fixed points of strongly Φ− hemi-contractive we extend the results to Mann-type iterative and Mann iteration process with errors.

scholarly journals On the Convergence of Mann and Ishikawa Iterative Processes for Asymptoticallyϕ-Strongly Pseudocontractive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Xuewu Wang ◽  
Giuseppe Marino ◽  
Luigi Muglia
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Iterative Process ◽  
Smooth Banach Space ◽  
Iterative Processes ◽  
Uniformly Smooth Banach Space ◽  
Pseudocontractive Mappings ◽  
Uniformly Smooth ◽  
Ishikawa Iterative Process

We prove the equivalence and the strong convergence of (1) the modified Mann iterative process and (2) the modified Ishikawa iterative process for asymptoticallyϕ-strongly pseudocontractive mappings in a uniformly smooth Banach space.

scholarly journals A Note on Implicit and Explicit Mann Iterative Processes for Asymptotically -Strongly Pseudocontractive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Luigi Muglia ◽  
Yonghong Yao
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Iterative Process ◽  
Smooth Banach Space ◽  
Iterative Processes ◽  
Uniformly Smooth Banach Space ◽  
Pseudocontractive Mappings ◽  
Uniformly Smooth ◽  
Implicit And Explicit

In this paper we prove the equivalence and the strong convergence of an explicit Mann iterative process and a modified implicit iterative process for asymptotically -strongly pseudocontractive mappings in a uniformly smooth Banach space.

scholarly journals Local solvability of a constrainedgradient system of total variation

2003 ◽  
Vol 2003 (6) ◽  
pp. 353-365 ◽  
Author(s):  
C. E. Chidume ◽  
H. Zegeye
Keyword(s):  
Banach Space ◽  
Iterative Methods ◽  
Total Variation ◽  
Local Solvability ◽  
Independent Interest ◽  
Smooth Banach Space ◽  
Uniformly Smooth Banach Space ◽  
Uniformly Smooth ◽  
Compact Subsets

SupposeXis a realq-uniformly smooth Banach space andF,K:X→XwithD(K)=F(X)=Xare accretive maps. Under various continuity assumptions onFandKsuch that0=u+KFuhas a solution, iterative methods which converge strongly to such a solution are constructed. No invertibility assumption is imposed onKand the operatorsKandFneed not be defined on compact subsets ofX. Our method of proof is of independent interest.

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