Weak and strong convergence theorems without some widely used conditions

Safeer Hussain Khan; Hafiz Fukhar-Ud-Din

Weak and strong convergence theorems without some widely used conditions

Safeer Hussain Khan
, Hafiz Fukhar-Ud-Din

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We establish weak (strong) convergence of Ishikawa iterates of two asymptotically (quasi-)nonexpansive maps without any condition on the rate of convergence associated with the two maps. Moreover, our weak convergence results do not require any of the Opial condition, Kadec-Klee property or Fréchet differentiable norm. © 2010 Academic Publications.

Original language	English
Pages (from-to)	137-148
Number of pages	12
Journal	International Journal of Pure and Applied Mathematics
Volume	63
Issue number	2
State	Published - Dec 10 2010

Keywords

Asymptotically (quasi-)nonexpansive map
Common fixed point
Demiclosedness
Ishikawa iteration process
Weak and strong convergence

Cite this

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title = "Weak and strong convergence theorems without some widely used conditions",

abstract = "We establish weak (strong) convergence of Ishikawa iterates of two asymptotically (quasi-)nonexpansive maps without any condition on the rate of convergence associated with the two maps. Moreover, our weak convergence results do not require any of the Opial condition, Kadec-Klee property or Fr{\'e}chet differentiable norm. {\textcopyright} 2010 Academic Publications.",

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AU - Khan, Safeer Hussain

AU - Fukhar-Ud-Din, Hafiz

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N2 - We establish weak (strong) convergence of Ishikawa iterates of two asymptotically (quasi-)nonexpansive maps without any condition on the rate of convergence associated with the two maps. Moreover, our weak convergence results do not require any of the Opial condition, Kadec-Klee property or Fréchet differentiable norm. © 2010 Academic Publications.

AB - We establish weak (strong) convergence of Ishikawa iterates of two asymptotically (quasi-)nonexpansive maps without any condition on the rate of convergence associated with the two maps. Moreover, our weak convergence results do not require any of the Opial condition, Kadec-Klee property or Fréchet differentiable norm. © 2010 Academic Publications.

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KW - Common fixed point

KW - Demiclosedness

KW - Ishikawa iteration process

KW - Weak and strong convergence

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JO - International Journal of Pure and Applied Mathematics

JF - International Journal of Pure and Applied Mathematics

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ER -

Weak and strong convergence theorems without some widely used conditions

Abstract

Keywords

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