scholarly journals Approximation of fixed point for multi-valued nonexpansive mapping in Banach spaces

2018 ◽  
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Banach Spaces

WEAK CONVERGENCE OF AN IMPLICIT ITERATIVE PROCESS WITH ERRORS FOR AN ASYMPTOTICALLY QUASI I-NONEXPANSIVE MAPPING IN BANACH SPACES

2011 ◽  
Vol 04 (02) ◽  
pp. 309-319 ◽  
Author(s):  
Farrukh Mukhamedov ◽  
Mansoor Saburov
Keyword(s):  
Fixed Point ◽  
Weak Convergence ◽  
Nonexpansive Mapping ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Iterative Process

In this paper we prove the weak convergence of the implicit iterative process with errors to a common fixed point of an asymptotically quasi I-nonexpansive mapping T and an asymptotically quasi-nonexpansive mapping I in Banach spaces.

scholarly journals Fixed-Point Theorems for Mean Nonexpansive Mappings in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhanfei Zuo
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Uniqueness Theorems ◽  
Existence And Uniqueness Theorems ◽  
Approximate Fixed Point

We define a mean nonexpansive mappingTonXin the sense thatTx-Ty≤ax-y+bx-Ty,a,b≥0,a+b≤1. It is proved that mean nonexpansive mapping has approximate fixed-point sequence, and, under some suitable conditions, we get some existence and uniqueness theorems of fixed point.

scholarly journals Three-Step Fixed Point Iteration for Generalized Multivalued Mapping in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Zhanfei Zuo
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Banach Spaces ◽  
Multivalued Mapping ◽  
Fixed Point Iteration ◽  
Iterative Processes ◽  
Multivalued Nonexpansive Mapping

The convergence of three-step fixed point iterative processes for generalized multivalued nonexpansive mapping was considered in this paper. Under some different conditions, the sequences of three-step fixed point iterates strongly or weakly converge to a fixed point of the generalized multivalued nonexpansive mapping. Our results extend and improve some recent results.

Convergence Theorems for Suzuki Generalized Nonexpansive Mapping in Banach Spaces

2021 ◽  
Vol 54 ◽  
Author(s):  
Abdulhamit Ekinci ◽  
Seyit Temir
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Convergence Theorems ◽  
Approximate Fixed Point ◽  
Strong Theorems ◽  
Numerical Example ◽  
Generalized Nonexpansive Mapping

In this paper, we study a new iterative scheme to approximate fixed point of Suzuki nonexpansive type mappings in Banach space. We also provesome weak and strong theorems for Suzuki nonexpansive typemappings. Numerical example is given to show the efficiency of newiteration process. The results obtained in this paper improve therecent ones announced by B. S. Thakur et al. \cite{Thakur}, Ullahand Arschad \cite{UA}.

scholarly journals Existence And Controllability Results For Fractional Control Systems In Reflexive Banach Spaces Using Fixed Point Theorem

2020 ◽  
Vol 17 (4) ◽  
pp. 1283
Author(s):  
Naseif Jasim AL-Jawari
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonexpansive Mapping ◽  
Control Systems ◽  
Banach Spaces ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Normal Structure ◽  
Reflexive Banach Spaces ◽  
Fractional Control

       In this paper, a fixed point theorem of nonexpansive mapping is established to study the existence and sufficient conditions for the controllability of nonlinear fractional control systems in reflexive Banach spaces. The result so obtained have been modified and developed in arbitrary space having Opial’s condition by using fixed point theorem deals with nonexpansive mapping defined on a set has normal structure. An application is provided to show the effectiveness of the obtained result.

Controllability for some nonlinear impulsive partial functional integrodifferential systems with infinite delay in Banach spaces

2020 ◽  
Vol 4 (2) ◽  
pp. 104-115
Author(s):  
Khalil Ezzinbi ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Resolvent Operator ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Mönch Fixed Point Theorem ◽  
The Resolvent Operator

This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.

On $\alpha$-nonexpansive mapping and fixed-points in Banach spaces

2018 ◽  
Vol 2018 (-) ◽  
Author(s):  
Prondanai Kaskasem ◽  
Chakkrid Klin-eam ◽  
Suthep Suantai
Keyword(s):  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Banach Spaces
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