scholarly journals H(., .)-φ-η-mixed accretive mapping with an application

2020 ◽  
Keyword(s):  
Accretive Mapping

scholarly journals The Meir-Keeler Type for Solving Variational Inequalities and Fixed Points of Nonexpansive Semigroups in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Phayap Katchang ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Strong Convergence Theorem ◽  
Accretive Mapping ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Nonexpansive Semigroups ◽  
Strongly Accretive Mapping

The aim of this paper is to introduce a new iterative scheme for finding common solutions of the variational inequalities for an inverse strongly accretive mapping and the solutions of fixed point problems for nonexpansive semigroups by using the modified viscosity approximation method associate with Meir-Keeler type mappings and obtain some strong convergence theorem in a Banach spaces under some parameters controlling conditions. Our results extend and improve the recent results of Li and Gu (2010), Wangkeeree and Preechasilp (2012), Yao and Maruster (2011), and many others.

scholarly journals Convergence of steepest descent approximation for set-valued quasi-accretive mapping equations

2000 ◽  
Vol 32 (10) ◽  
pp. 1083-1093 ◽  
Author(s):  
N.-J. Huang ◽  
Y.J. Cho ◽  
M.-R. Bai ◽  
S.M. Kang
Keyword(s):  
Steepest Descent ◽  
Accretive Mapping

scholarly journals Iterative approximation of a solution of a general variational-like inclusion in Banach spaces

2004 ◽  
Vol 2004 (22) ◽  
pp. 1159-1168 ◽  
Author(s):  
C. E. Chidume ◽  
K. R. Kazmi ◽  
H. Zegeye
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Real Banach Space ◽  
Accretive Mapping ◽  
Convergence Criteria ◽  
Iterative Approximation ◽  
Proximal Point ◽  
Point Mapping ◽  
Lipschitz Continuous ◽  
Accretive Mappings

We introduce a class ofη-accretive mappings in a real Banach space and show that theη-proximal point mapping forη-m-accretive mapping is Lipschitz continuous. Further, we develop an iterative algorithm for a class of general variational-like inclusions involvingη-accretive mappings in real Banach space, and discuss its convergence criteria. The class ofη-accretive mappings includes several important classes of operators that have been studied by various authors.

Variational inclusion governed by αβ-H((.,.),(.,.))-mixed accretive mapping

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6529-6542
Author(s):  
Sanjeev Gupta ◽  
Shamshad Husain ◽  
Vishnu Mishra
Keyword(s):  
Banach Spaces ◽  
Iterative Algorithm ◽  
Lipschitz Continuity ◽  
Variational Inclusion ◽  
Variational Inclusions ◽  
Accretive Mapping ◽  
Proximal Point ◽  
Point Mapping ◽  
Accretive Mappings

In this paper, we look into a new concept of accretive mappings called ??-H((.,.),(.,.))-mixed accretive mappings in Banach spaces. We extend the concept of proximal-point mappings connected with generalized m-accretive mappings to the ??-H((.,.),(.,.))-mixed accretive mappings and discuss its characteristics like single-valuable and Lipschitz continuity. Some illustration are given in support of ??-H((.,.),(.,.))-mixed accretive mappings. Since proximal point mapping is a powerful tool for solving variational inclusion. Therefore, As an application of introduced mapping, we construct an iterative algorithm to solve variational inclusions and show its convergence with acceptable assumptions.

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