Geodesic
Convergence Theorems of a Scheme for $I$-Asymptotically Quasi-Nonexpansive Type Mapping in Banach Space
Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 239 .

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Let $X$ be a Banach space. Let $K$ be a nonempty subset of $X$. Let $T:K\to K$ be an $I$-asymptotically quasi-nonexpansive type mapping and $I:K\to K$ be an asymptotically quasi-nonexpansive type mappings in the Banach space. Our aim is to establish the necessary and sufficient conditions for the convergence of the Ishikawa iterative sequences with errors of an $I$-asymptotically quasi-nonexpansive type mappping in Banach spaces to a common fixed point of $T$ and $I$. Also, we study the convergence of the Ishikawa iterative sequences to common fixed point for nonself $I$-asymptotically quasi-nonexpansive type mapping in Banach spaces. The results presented in this paper extend and generalize some recent work of Chang and Zhou [1], Wang [19], Yao and Wang [20] and many others.
DOI : 10.2298/PIM130818001T
Classification : 47H09, 47H10
Keywords: I-asymptotically quasi-nonexpansive type mapping, nonself I-asymptotically quasi-nonexpansive type mapping, Ishikawa iterative schemes 
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     author = {Seyit Temir},
     title = {Convergence {Theorems} of a {Scheme} for $I${-Asymptotically} {Quasi-Nonexpansive} {Type} {Mapping} in {Banach} {Space}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {239 },
     publisher = {mathdoc},
     volume = {_N_S_97},
     number = {111},
     year = {2015},
     doi = {10.2298/PIM130818001T},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM130818001T/}
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Seyit Temir. Convergence Theorems of a Scheme for $I$-Asymptotically Quasi-Nonexpansive Type Mapping in Banach Space. Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 239 . doi : 10.2298/PIM130818001T. http://geodesic.mathdoc.fr/articles/10.2298/PIM130818001T/

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