scholarly journals An evolution equation governed by a quasi-nonexpansive mapping on Hadamard manifolds and its backward discretization

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2217-2224
Author(s):  
Hadi Khatibzadeh ◽  
Mohsen Piranfar
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Evolution Equation ◽  
Nonexpansive Mapping ◽  
Nonexpansive Mappings ◽  
Time Discretization ◽  
Asymptotic Behavior Of Solutions ◽  
Hadamard Manifolds ◽  
First Order ◽  
Locally Lipschitz

We study the asymptotic behavior of solutions to a first-order evolution equation governed by a locally Lipschitz quasi-nonexpansive mapping. We show that such solutions converge to a fixed point of the quasi-nonexpansive mapping as time goes to infinity. Time discretization of this system provides an iterative method to approximate a fixed point of quasi-nonexpansive mappings on Hadamard manifolds.

scholarly journals Strong convergence for nonexpansive mappings by viscosity approximation methods in Hadamard manifolds

2015 ◽  
Vol 4 (2) ◽  
pp. 299
Author(s):  
Mandeep Kumari ◽  
Renu Chugh
Keyword(s):  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Approximation Method ◽  
Nonexpansive Mappings ◽  
Approximation Methods ◽  
Hadamard Manifolds ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Viscosity Approximation Methods

<p>In 2010, Victoria Martin Marquez studied a nonexpansive mapping in Hadamard manifolds using Viscosity approximation method. Our goal in this paper is to study the strong convergence of the Viscosity approximation method in Hadamard manifolds. Our results improve and extend the recent research in the framework of Hadamard manifolds.</p>

scholarly journals Asymptotic Behavior of Solutions to Abstract Stochastic Fractional Partial Integrodifferential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhi-Han Zhao ◽  
Yong-Kui Chang ◽  
Juan J. Nieto
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Integrodifferential Equation ◽  
Fixed Point Theorems ◽  
Mild Solutions ◽  
Integrodifferential Equations ◽  
Linear Operators ◽  
Asymptotic Behavior Of Solutions ◽  
Almost Automorphic ◽  
Partial Integrodifferential Equation

The existence of asymptotically almost automorphic mild solutions to an abstract stochastic fractional partial integrodifferential equation is considered. The main tools are some suitable composition results for asymptotically almost automorphic processes, the theory of sectorial linear operators, and classical fixed point theorems. An example is also given to illustrate the main theorems.

The Strong Convergence of a New Iterative Algorithm for Asymptotically Nonexpansive Mappings

2013 ◽  
Vol 756-759 ◽  
pp. 3628-3633
Author(s):  
Yuan Heng Wang ◽  
Wei Wei Sun
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Iterative Algorithm ◽  
Real Banach Space ◽  
Nonexpansive Mappings ◽  
Iterative Sequence ◽  
Asymptotically Nonexpansive ◽  
Differentiable Norm

In a real Banach space E with a uniformly differentiable norm, we prove that a new iterative sequence converges strongly to a fixed point of an asymptotically nonexpansive mapping. The results in this paper improve and extend some recent results of other authors.

scholarly journals Mann iteration process for monotone nonexpansive mappings with a graph

2019 ◽  
Vol 26 (4) ◽  
pp. 629-636
Author(s):  
Monther Rashed Alfuraidan
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Convex Subset ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Mann Iteration ◽  
Iteration Sequence ◽  
Mann Iteration Process ◽  
Monotone Nonexpansive Mapping

Abstract Let {(X,\lVert\,\cdot\,\rVert)} be a Banach space. Let C be a nonempty, bounded, closed and convex subset of X and let {T:C\rightarrow C} be a G-monotone nonexpansive mapping. In this work, it is shown that the Mann iteration sequence defined by x_{n+1}=t_{n}T(x_{n})+(1-t_{n})x_{n},\quad n=1,2,\dots, proves the existence of a fixed point of G-monotone nonexpansive mappings.

scholarly journals Existence and asymptotic behavior of solutions for neutral stochastic partial integrodifferential equations with infinite delays

2016 ◽  
Vol 16 (06) ◽  
pp. 1650014 ◽  
Author(s):  
Mamadou Abdoul Diop ◽  
Tomás Caraballo ◽  
Mahamat Mahamat Zene
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Resolvent Operators ◽  
Infinite Delays ◽  
Fixed Point Principle ◽  
Exponentially Stable

In this work we study the existence, uniqueness and asymptotic behavior of mild solutions for neutral stochastic partial integrodifferential equations with infinite delays. To prove the results, we use the theory of resolvent operators as developed by R. Grimmer [13], as well as a version of the fixed point principle. We establish sufficient conditions ensuring that the mild solutions are exponentially stable in [Formula: see text]th-moment. An example is provided to illustrate the abstract results.

scholarly journals Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spaces

2005 ◽  
Vol 2005 (11) ◽  
pp. 1685-1692 ◽  
Author(s):  
Somyot Plubtieng ◽  
Rabian Wangkeeree
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Convex Subset ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Nonempty Closed Convex Subset ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Completely Continuous

Suppose thatCis a nonempty closed convex subset of a real uniformly convex Banach spaceX. LetT:C→Cbe an asymptotically quasi-nonexpansive mapping. In this paper, we introduce the three-step iterative scheme for such map with error members. Moreover, we prove that ifTis uniformlyL-Lipschitzian and completely continuous, then the iterative scheme converges strongly to some fixed point ofT.

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