A fixed point theorem for asymptotically nonexpansive type mappings in uniformly convex Banach spaces

2017 ◽  
Vol 26 (1) ◽  
pp. 9-14
Author(s):  
V. Sankar Raj ◽  
S. Jamal Fathima
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Uniformly Convex ◽  
Uniformly Convex Banach Spaces ◽  
Asymptotically Nonexpansive

scholarly journals Fixed point approximation of Presic nonexpansive mappings in product of CAT (0) spaces

2016 ◽  
Vol 32 (3) ◽  
pp. 315-322
Author(s):  
HAFIZ FUKHAR-UD-DIN ◽  
◽  
VASILE BERINDE ◽  
ABDUL RAHIM KHAN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Banach Spaces ◽  
Point Theorem ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Control Parameters ◽  
Uniformly Convex ◽  
Uniformly Convex Banach Spaces

We obtain a fixed point theorem for Presiˇ c nonexpansive mappings on the product of ´ CAT (0) spaces and approximate this fixed points through Ishikawa type iterative algorithms under relaxed conditions on the control parameters. Our results are new in the literature and are valid in uniformly convex Banach spaces.

Approximating common fixed point of asymptotically nonexpansive mappings without convergence condition

2017 ◽  
Vol 33 (3) ◽  
pp. 327-334
Author(s):  
ABDUL RAHIM KHAN ◽  
◽  
HAFIZ FUKHAR-UD-DIN ◽  
NUSRAT YASMIN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Convergence Condition ◽  
Finite Family ◽  
Uniformly Convex ◽  
Asymptotically Nonexpansive Mappings ◽  
Uniformly Convex Banach Spaces ◽  
Asymptotically Nonexpansive

In the context of a hyperbolic space, we introduce and study convergence of an implicit iterative scheme of a finite family of asymptotically nonexpansive mappings without convergence condition. The results presented substantially improve and extend several well-known resullts in uniformly convex Banach spaces.

scholarly journals Existence and approximation of fixed points in convex metric spaces

2014 ◽  
Vol 30 (2) ◽  
pp. 175-185
Author(s):  
HAFIZ FUKHAR-UD-DIN ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Uniformly Convex Banach Spaces ◽  
Convex Metric Spaces ◽  
Asymptotically Nonexpansive ◽  
Generalized Nonexpansive Mapping ◽  
The Fixed Point Theorem

A fixed point theorem for a generalized nonexpansive mapping is established in a convex metric space introduced by Takahashi [A convexity in metric spaces and nonexpansive mappings, Kodai Math. Sem. Rep., 22 (1970), 142–149]. Our theorem generalizes simultaneously the fixed point theorem of Bose and Laskar [Fixed point theorems for certain class of mappings, Jour. Math. Phy. Sci., 19 (1985), 503–509] and the well-known fixed point theorem of Goebel and Kirk [A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171–174] on a nonlinear domain. The fixed point obtained is approximated by averaging Krasnosel’skii iterations of the mapping. Our results substantially improve and extend several known results in uniformly convex Banach spaces and CAT(0) spaces.

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