scholarly journals Approximating Fixed Points of The General Asymptotic Set Valued Mappings

2020 ◽  
Vol 18 ◽  
pp. 52-59
Author(s):  
Salwa Salman Abed
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Existence Theorem ◽  
Banach Spaces ◽  
Reflexive Banach Spaces ◽  
Set Valued Mapping ◽  
Set Valued Mappings ◽  
Fixed Point Iterative Method

  The purpose of this paper is to introduce a new generalization of asymptotically non-expansive set-valued mapping  and to discuss its demi-closeness principle. Then, under certain conditions, we prove that the sequence defined by  yn+1 = tn z+ (1-tn )un ,  un in Gn( yn ) converges strongly to some fixed point in reflexive Banach spaces.  As an application, existence theorem for an iterative differential equation as well as convergence theorems for a fixed point iterative method designed to approximate this solution is proved

scholarly journals Approximating fixed points of demicontractive mappings by iterative methods defined as admissible perturbations

2016 ◽  
Vol 25 (1) ◽  
pp. 121-126
Author(s):  
CRISTINA TICALA ◽  
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Convergence Theorems ◽  
Admissible Perturbation ◽  
Demicontractive Operator ◽  
Demicontractive Mappings ◽  
Fixed Point Iterative Method

The aim of this paper is to prove some convergence theorems for a general Krasnoselskij type fixed point iterative method defined by means of the concept of admissible perturbation of a demicontractive operator in Hilbert spaces.

Approximating fixed points of demicontractive mappings by iterative methods defined as admissible perturbations

2016 ◽  
Vol 25 (1) ◽  
pp. 121-126
Author(s):  
CRISTINA TICALA ◽  
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Convergence Theorems ◽  
Admissible Perturbation ◽  
Demicontractive Operator ◽  
Demicontractive Mappings ◽  
Fixed Point Iterative Method

The aim of this paper is to prove some convergence theorems for a general Krasnoselskij type fixed point iterative method defined by means of the concept of admissible perturbation of a demicontractive operator in Hilbert spaces.

scholarly journals Approximation of the Fixed Point of Multivalued Quasi-Nonexpansive Mappings via a Faster Iterative Process with Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Godwin Amechi Okeke ◽  
Mujahid Abbas ◽  
Manuel de la Sen
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Boundary Value Problems ◽  
Rate Of Convergence ◽  
Iterative Process ◽  
Numerical Experiments ◽  
Nonexpansive Mappings ◽  
Point Boundary ◽  
Fixed Point Iterative Method

In this paper, we approximate the fixed points of multivalued quasi-nonexpansive mappings via a faster iterative process and propose a faster fixed-point iterative method for finding the solution of two-point boundary value problems. We prove analytically and with series of numerical experiments that the Picard–Ishikawa hybrid iterative process has the same rate of convergence as the CR iterative process.

Approximating fixed points of asymptotically demicontractive mappings by iterative schemes defined as admissible perturbations

2017 ◽  
Vol 33 (3) ◽  
pp. 381-388
Author(s):  
CRISTINA TICALA ◽  
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Closed Subset ◽  
Convergence Theorems ◽  
Iterative Schemes ◽  
Demicontractive Operator ◽  
Demicontractive Mappings ◽  
Fixed Point Iterative Method

We establish convergence theorems for a Krasnoselskij type fixed point iterative method constructed as the admissible perturbation of an asymptotically demicontractive operator defined on a convex closed subset of a Hilbert space.

scholarly journals Random fixed points of non-self maps and random approximations

1997 ◽  
Vol 10 (2) ◽  
pp. 127-130 ◽  
Author(s):  
Ismat Beg
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Approximation Theorem ◽  
Random Operators ◽  
Reflexive Banach Spaces ◽  
Random Fixed Point ◽  
Random Fixed Points

In this paper we prove random fixed point theorems in reflexive Banach spaces for nonexpansive random operators satisfying inward or Leray-Schauder condition and establish a random approximation theorem.

scholarly journals A Study of Nonlinear Boundary Value Problem

2021 ◽  
Author(s):  
Noureddine Bouteraa ◽  
Habib Djourdem
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Iterative Method ◽  
Boundary Value Problem ◽  
Higher Order ◽  
Nonlinear Boundary Value Problem ◽  
Point Boundary ◽  
Error Estimations ◽  
Fractional Differential

In this chapter, firstly we apply the iterative method to establish the existence of the positive solution for a type of nonlinear singular higher-order fractional differential equation with fractional multi-point boundary conditions. Explicit iterative sequences are given to approximate the solutions and the error estimations are also given. Secondly, we cover the multi-valued case of our problem. We investigate it for nonconvex compact valued multifunctions via a fixed point theorem for multivalued maps due to Covitz and Nadler. Two illustrative examples are presented at the end to illustrate the validity of our results.

scholarly journals F-Metric, F-Contraction and Common Fixed-Point Theorems with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 586 ◽  
Author(s):  
Awais Asif ◽  
Muhammad Nazam ◽  
Muhammad Arshad ◽  
Sang Og Kim
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Third ◽  
Set Valued Mappings ◽  
Common Fixed Point Theorems

In this paper, we noticed that the existence of fixed points of F-contractions, in F -metric space, can be ensured without the third condition (F3) imposed on the Wardowski function F : ( 0 , ∞ ) → R . We obtain fixed points as well as common fixed-point results for Reich-type F-contractions for both single and set-valued mappings in F -metric spaces. To show the usability of our results, we present two examples. Also, an application to functional equations is presented. The application shows the role of fixed-point theorems in dynamic programming, which is widely used in computer programming and optimization. Our results extend and generalize the previous results in the existing literature.

scholarly journals Fixed Point Problems for Nonexpansive Mappings in Bounded Sets of Banach Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Xianbing Wu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Process ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Fixed Point Problems ◽  
Bounded Sets

It is well known that nonexpansive mappings do not always have fixed points for bounded sets in Banach space. The purpose of this paper is to establish fixed point theorems of nonexpansive mappings for bounded sets in Banach spaces. We study the existence of fixed points for nonexpansive mappings in bounded sets, and we present the iterative process to approximate fixed points. Some examples are given to support our results.

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