Firmly nonexpansive and Kirszbraun-Valentine extensions: a constructive approach via monotone operator theory [PDF]
arXiv, 2008 Utilizing our recent proximal-average based results on the constructive extension of monotone operators, we provide a novel approach to the celebrated Kirszbraun-Valentine Theorem and to the extension of firmly nonexpansive mappings.
arxiv
Alternative iterative methods for nonexpansive mappings, rates of convergence and application [PDF]
arXiv, 2009 Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such iterations using proof-theoretic techniques. Some applications of the convergence results are presented.
arxiv
Stability data dependency and errors estimation for a general iteration method
Alexandria Engineering Journal, 2021 In this paper, we present a result of stability, data Dependency and errors estimation for D Iteration Method. We also prove that errors in D iterative process is controllable. Especially stability, data dependence, controllability, error accumulation of
Aftab Hussain +2 more
doaj
Fixed point theorems for a class of mappings depending of another function and defined on cone metric spaces [PDF]
arXiv, 2009 In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.
arxiv
Comments on relaxed $(γ, r)$-cocoercive mappings [PDF]
arXiv, 2009 We show that the variational inequality $VI(C,A)$ has a unique solution for a relaxed $(\gamma, r)$-cocoercive, $\mu$-Lipschitzian mapping $A: C\to H$ with $r>\gamma \mu^2$, where $C$ is a nonempty closed convex subset of a Hilbert space $H$. From this result, it can be derived that, for example, the recent algorithms given in the references of this ...
arxiv
Fixed point results for generalized convex orbital Lipschitz operators
Demonstratio MathematicaKrasnoselskii’s iteration is a classical and important method for approximating the fixed point of an operator that satisfies certain conditions. Many authors have used this approach to obtain several famous fixed point theorems for different types of ...
Zhou Mi +4 more
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On the Existence of Fixed Points of Contraction Mappings Depending of Two Functions on Cone Metric Spaces [PDF]
Bull. Iranian Math. Soc., 40(3) (2014), 689--698, 2009 In this paper, we study the existence of fixed points for mappings defined on complete, (sequentially compact) cone metric spaces, satisfying a general contractive inequality depending of two additional mappings.
arxiv
A Solution of variational inequality problem for a finite family of nonexpansive mappings in Hilbert spaces [PDF]
JP Jour. Fixed Point Theory Appl. 5(2010), N.3, 157-170, 2010 In this paper we prove the strong convergence of the explicit iterative process to a common fixed point of the finite family of nonexpansive mappings defined on Hilbert space, which solves the the variational inequality on the fixed points set.
arxiv
Proximal quasi-normal structure in convex metric spaces
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 We consider, in the setting of convex metric spaces, a new class of Kannan type cyclic orbital contractions, and study the existence of its best proximity points.
Gabeleh Moosa
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Moving closer: contractive maps on discrete metric spaces and graphs [PDF]
arXiv, 2010 We consider discrete metric spaces and we look for non-constant contractions. We introduce the notion of contractive map and we characterize the spaces with non-constant contractive maps. We provide some examples to discussion the possible relations between contractions, contractive maps and constant functions.
arxiv