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Volume 31, Issue 1
Weak Convergence Theorems for Nonself Mappings

Yongquan Liu & Weiping Guo

Commun. Math. Res., 31 (2015), pp. 15-22.

Published online: 2021-05

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  • Abstract

Let $E$ be a real uniformly convex and smooth Banach space, and $K$ be a nonempty closed convex subset of $E$ with $P$ as a sunny nonexpansive retraction. Let $T_1, T_2 : K → E$ be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with a sequence $\{k^{(i)}_n\} ⊂ [1, ∞) (i = 1, 2)$, and $F := F(T_1) ∩ F(T_2) ≠ ∅$. An iterative sequence for approximation common fixed points of the two nonself asymptotically nonexpansive mappings is discussed. If $E$ also has a Fréchet differentiable norm or its dual $E^∗$ has Kadec-Klee property, then weak convergence theorems are obtained.

  • Keywords

asymptotically nonexpansive nonself-mapping, weak convergence, uniformly convex Banach space, common fixed point, smooth Banach space.

  • AMS Subject Headings

47H09, 47H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-31-15, author = {Yongquan and Liu and and 18591 and and Yongquan Liu and Weiping and Guo and and 18592 and and Weiping Guo}, title = {Weak Convergence Theorems for Nonself Mappings}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {31}, number = {1}, pages = {15--22}, abstract = {

Let $E$ be a real uniformly convex and smooth Banach space, and $K$ be a nonempty closed convex subset of $E$ with $P$ as a sunny nonexpansive retraction. Let $T_1, T_2 : K → E$ be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with a sequence $\{k^{(i)}_n\} ⊂ [1, ∞) (i = 1, 2)$, and $F := F(T_1) ∩ F(T_2) ≠ ∅$. An iterative sequence for approximation common fixed points of the two nonself asymptotically nonexpansive mappings is discussed. If $E$ also has a Fréchet differentiable norm or its dual $E^∗$ has Kadec-Klee property, then weak convergence theorems are obtained.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2015.01.02}, url = {http://global-sci.org/intro/article_detail/cmr/18945.html} }
TY - JOUR T1 - Weak Convergence Theorems for Nonself Mappings AU - Liu , Yongquan AU - Guo , Weiping JO - Communications in Mathematical Research VL - 1 SP - 15 EP - 22 PY - 2021 DA - 2021/05 SN - 31 DO - http://doi.org/10.13447/j.1674-5647.2015.01.02 UR - https://global-sci.org/intro/article_detail/cmr/18945.html KW - asymptotically nonexpansive nonself-mapping, weak convergence, uniformly convex Banach space, common fixed point, smooth Banach space. AB -

Let $E$ be a real uniformly convex and smooth Banach space, and $K$ be a nonempty closed convex subset of $E$ with $P$ as a sunny nonexpansive retraction. Let $T_1, T_2 : K → E$ be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with a sequence $\{k^{(i)}_n\} ⊂ [1, ∞) (i = 1, 2)$, and $F := F(T_1) ∩ F(T_2) ≠ ∅$. An iterative sequence for approximation common fixed points of the two nonself asymptotically nonexpansive mappings is discussed. If $E$ also has a Fréchet differentiable norm or its dual $E^∗$ has Kadec-Klee property, then weak convergence theorems are obtained.

Yongquan Liu & Weiping Guo. (2021). Weak Convergence Theorems for Nonself Mappings. Communications in Mathematical Research . 31 (1). 15-22. doi:10.13447/j.1674-5647.2015.01.02
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