A fixed point theorem for local pseudo-contractions in uniformly convex spaces

1979 ◽  
Vol 30 (1) ◽  
pp. 89-102 ◽  
Author(s):  
W. A. Kirk
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Uniformly Convex ◽  
Uniformly Convex Spaces ◽  
Convex Spaces

scholarly journals An extension of a theorem of Sahab, Khan, and Sessa

2001 ◽  
Vol 27 (11) ◽  
pp. 701-706 ◽  
Author(s):  
A. R. Khan ◽  
N. Hussain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Locally Convex Spaces ◽  
Invariant Approximation ◽  
Recent Theorem ◽  
Locally Convex ◽  
Convex Spaces

A fixed point theorem of Fisher and Sessa is generalized to locally convex spaces and the new result is applied to extend a recent theorem on invariant approximation of Sahab, Khan, and Sessa.

scholarly journals Vector Variational Inequalities In G-Convex Spaces

2021 ◽  
Vol 53 ◽  
Author(s):  
Maryam Salehnejad ◽  
Mahdi Azhini
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Fixed Point Theorem ◽  
Variational Inequalities ◽  
Point Theorem ◽  
Vector Variational Inequality ◽  
Vector Variational Inequalities ◽  
Kkm Theorem ◽  
Convex Spaces

Inthispaper,westudysomeexistencetheoremsofsolutionsforvectorvariational inequality by using the generalized KKM theorem. Also, we investigate the properties of so- lution set of the Minty vector variational inequality in G–convex spaces. Finally, we prove the equivalence between a Browder fixed point theorem type and the vector variational in- equality in G-convex spaces.

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.

scholarly journals $$\alpha $$-Firmly nonexpansive operators on metric spaces

2022 ◽  
Vol 24 (1) ◽  
Author(s):  
Arian Bërdëllima ◽  
Florian Lauster ◽  
D. Russell Luke
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Convergence Analysis ◽  
Metric Spaces ◽  
Uniformly Convex ◽  
Point Mapping ◽  
Splitting Algorithms ◽  
Uniformly Convex Spaces ◽  
Cluster Points ◽  
Convex Spaces

AbstractWe extend to p-uniformly convex spaces tools from the analysis of fixed point iterations in linear spaces. This study is restricted to an appropriate generalization of single-valued, pointwise averaged mappings. Our main contribution is establishing a calculus for these mappings in p-uniformly convex spaces, showing in particular how the property is preserved under compositions and convex combinations. This is of central importance to splitting algorithms that are built by such convex combinations and compositions, and reduces the convergence analysis to simply verifying that the individual components have the required regularity pointwise at fixed points of the splitting algorithms. Our convergence analysis differs from what can be found in the previous literature in that the regularity assumptions are only with respect to fixed points. Indeed we show that, if the fixed point mapping is pointwise nonexpansive at all cluster points, then these cluster points are in fact fixed points, and convergence of the sequence follows. Additionally, we provide a quantitative convergence analysis built on the notion of gauge metric subregularity, which we show is necessary for quantifiable convergence estimates. This allows one for the first time to prove convergence of a tremendous variety of splitting algorithms in spaces with curvature bounded from above.

scholarly journals Convergence of proximal splitting algorithms in $\operatorname{CAT}(\kappa)$ spaces and beyond

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Florian Lauster ◽  
D. Russell Luke
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Uniformly Convex ◽  
Metric Subregularity ◽  
Splitting Algorithms ◽  
Projected Gradients ◽  
Fixed Point Iterations ◽  
Uniformly Convex Spaces ◽  
Convex Spaces

AbstractIn the setting of $\operatorname{CAT}(\kappa)$ CAT ( κ ) spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky–Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric subregularity. Linear metric subregularity is in any case necessary for linearly convergent fixed point sequences, so the result is tight. To show this, we develop a theory of fixed point mappings that violate the usual assumptions of nonexpansiveness and firm nonexpansiveness in p-uniformly convex spaces.

Some Fixed Point Theorems in Metrically Convex Spaces

2000 ◽  
Vol 7 (3) ◽  
pp. 523-530 ◽  
Author(s):  
M. S. Khan ◽  
H. K. Pathak ◽  
M. D. Khan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Convex Metric Space ◽  
Convex Spaces

Abstract A fixed point theorem is proved in a complete metrically convex metric space. Our result generalizes the theorems of Assad [Tamkang J. Math. 7: 91–94, 1976] and Chatterjea [C.R. Acad., Bulgare Sci. 25: 727–730, 1972].

scholarly journals A Collectively Fixed Point Theorem in Abstract Convex Spaces and Its Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Haishu Lu ◽  
Qingwen Hu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Theorems ◽  
Abstract Economies ◽  
Collectively Fixed Point ◽  
Convex Spaces

The main purpose of this paper is to establish a new collectively fixed point theorem in noncompact abstract convex spaces. As applications of this theorem, we obtain some new existence theorems of equilibria for generalized abstract economies in noncompact abstract convex spaces.

scholarly journals A fixed point theorem in locally convex spaces

2010 ◽  
Vol 61 (2) ◽  
pp. 223-239 ◽  
Author(s):  
Vladimir Kozlov ◽  
Johan Thim ◽  
Bengt Ove Turesson
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Locally Convex Spaces ◽  
Locally Convex ◽  
Convex Spaces
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