scholarly journals On some fixed point theorems on uniformly convex Banach spaces

1992 ◽  
Vol 167 (1) ◽  
pp. 160-166 ◽  
Author(s):  
P Veeramani
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Uniformly Convex ◽  
Uniformly Convex Banach Spaces

scholarly journals Fixed point theorems for generalized Lipschitzian semigroups in Banach spaces

1999 ◽  
Vol 22 (1) ◽  
pp. 119-129
Author(s):  
Balwant Singh Thakur ◽  
Jong Soo Jung
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Hardy Space ◽  
Banach Spaces ◽  
Sobolev Spaces ◽  
Fixed Point Theorems ◽  
Uniformly Convex ◽  
Uniformly Convex Banach Spaces

Fixed point theorems for generalized Lipschitzian semigroups are proved inp-uniformly convex Banach spaces and in uniformly convex Banach spaces. As applications, its corollaries are given in a Hilbert space, inLpspaces, in Hardy spaceHp, and in Sobolev spacesHk,p, for1<p<∞andk≥0.

scholarly journals Fixed point theorems in uniformly rotund metric spaces

1976 ◽  
Vol 14 (2) ◽  
pp. 181-192 ◽  
Author(s):  
John Staples
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Linear Structure ◽  
Uniform Convexity ◽  
Uniformly Convex ◽  
Underlying Space ◽  
Uniformly Convex Banach Spaces ◽  
Definition Of

In recent years fixed point theorems have been proved for non-expansive and similar mappings on uniformly convex Banach spaces. The only role the linear structure plays in the statement of these results occurs in the definition of uniform convexity. It is therefore natural to ask whether the results depend essentially on the linear structure, or whether an extension of the notion of uniform convexity to metric spaces would allow the hypothesis of linear structure on the underlying space to be removed.

scholarly journals Common fixed point iterations for a class of multi-valued mappings in $$\mathbf {CAT}(0)$$ spaces

2020 ◽  
Vol 9 (3) ◽  
pp. 681-690
Author(s):  
Khairul Saleh ◽  
Hafiz Fukhar-ud-din
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Uniformly Convex ◽  
Uniformly Convex Banach Spaces ◽  
Fixed Point Iterations

Abstract In this work, we propose an iterative scheme to approach common fixed point(s) of a finite family of generalized multi-valued nonexpansive mappings in a CAT(0) space. We establish and prove convergence theorems for the algorithm. The results are new and interesting in the theory of $$CAT\left( 0\right) $$ C A T 0 spaces and are the analogues of corresponding ones in uniformly convex Banach spaces and Hilbert spaces.

scholarly journals Convergence of Ishikawa iterates of generalized nonexpansive mappings

1997 ◽  
Vol 20 (3) ◽  
pp. 517-520 ◽  
Author(s):  
M. K. Ghosh ◽  
L. Debnath
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Uniformly Convex ◽  
Strictly Convex ◽  
Strictly Convex Banach Spaces

This paper is concerned with the convergence of Ishikawa iterates of generalized nonexpansive mappings in both uniformly convex and strictly convex Banach spaces. Several fixed point theorems are discussed.

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.

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