Admissible perturbations of alpha-psi-pseudocontractive operators: convergence theorems

Risultato della ricerca: Other

Abstract

In the last decades, the study of convergence of fixed point iterative methods has received an increasing attention, due to their performance as tools for solving numerical problems. As a consequence of this fact, one can access to a wide literature on iterative schemes involving different types of operators; see [2, 4, 5]. We point out that fixed point iterative approximation methods have been largely applied in dealing with stability and convergence problems; see [1, 6]. In particular, we refer to various control and optimization questions arising in pure and applied sciences involving dynamical systems, where the problem in study can be easily arranged as a fixed point problem. Then, we prove some convergence theorems for a certain class of operators in real Hilbert spaces. Precisely, by using the concept of admissible perturbation of alpha-psi-pseudocontractive operators in Hilbert spaces, we establish results for Krasnoselskij type fixed point iterativeschemes. Our theorems complement, generalize and unify some existing results; see [3, 4].
Lingua originaleEnglish
Pagine104-104
Numero di pagine1
Stato di pubblicazionePublished - 2015

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Convergence Theorem
Perturbation
Operator
Hilbert space
Fixed point
Iteration
Fixed Point Method
Fixed Point Problem
Stability and Convergence
Iterative Scheme
Approximation Methods
Complement
Dynamical system
Generalise
Optimization
Theorem
Concepts
Class

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title = "Admissible perturbations of alpha-psi-pseudocontractive operators: convergence theorems",
abstract = "In the last decades, the study of convergence of fixed point iterative methods has received an increasing attention, due to their performance as tools for solving numerical problems. As a consequence of this fact, one can access to a wide literature on iterative schemes involving different types of operators; see [2, 4, 5]. We point out that fixed point iterative approximation methods have been largely applied in dealing with stability and convergence problems; see [1, 6]. In particular, we refer to various control and optimization questions arising in pure and applied sciences involving dynamical systems, where the problem in study can be easily arranged as a fixed point problem. Then, we prove some convergence theorems for a certain class of operators in real Hilbert spaces. Precisely, by using the concept of admissible perturbation of alpha-psi-pseudocontractive operators in Hilbert spaces, we establish results for Krasnoselskij type fixed point iterativeschemes. Our theorems complement, generalize and unify some existing results; see [3, 4].",
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N2 - In the last decades, the study of convergence of fixed point iterative methods has received an increasing attention, due to their performance as tools for solving numerical problems. As a consequence of this fact, one can access to a wide literature on iterative schemes involving different types of operators; see [2, 4, 5]. We point out that fixed point iterative approximation methods have been largely applied in dealing with stability and convergence problems; see [1, 6]. In particular, we refer to various control and optimization questions arising in pure and applied sciences involving dynamical systems, where the problem in study can be easily arranged as a fixed point problem. Then, we prove some convergence theorems for a certain class of operators in real Hilbert spaces. Precisely, by using the concept of admissible perturbation of alpha-psi-pseudocontractive operators in Hilbert spaces, we establish results for Krasnoselskij type fixed point iterativeschemes. Our theorems complement, generalize and unify some existing results; see [3, 4].

AB - In the last decades, the study of convergence of fixed point iterative methods has received an increasing attention, due to their performance as tools for solving numerical problems. As a consequence of this fact, one can access to a wide literature on iterative schemes involving different types of operators; see [2, 4, 5]. We point out that fixed point iterative approximation methods have been largely applied in dealing with stability and convergence problems; see [1, 6]. In particular, we refer to various control and optimization questions arising in pure and applied sciences involving dynamical systems, where the problem in study can be easily arranged as a fixed point problem. Then, we prove some convergence theorems for a certain class of operators in real Hilbert spaces. Precisely, by using the concept of admissible perturbation of alpha-psi-pseudocontractive operators in Hilbert spaces, we establish results for Krasnoselskij type fixed point iterativeschemes. Our theorems complement, generalize and unify some existing results; see [3, 4].

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UR - http://lan.unical.it/NETNA2015/

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