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.

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.

scholarly journals A New System of Random Generalized Variational Inclusions with Random Fuzzy Mappings and Random --Accretive Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Sayyedeh Zahra Nazemi
Keyword(s):  
Banach Spaces ◽  
Iterative Algorithm ◽  
Resolvent Operator ◽  
Lipschitz Continuity ◽  
Variational Inclusions ◽  
Accretive Mappings ◽  
New System

We introduce a new notion of random --accretive mappings and prove the Lipschitz continuity of the random resolvent operator associated with the random --accretive mappings. We introduce and study a new system of random generalized variational inclusions with random --accretive mappings and random fuzzy mappings in Banach spaces. By using the random resolvent operator, an iterative algorithm for solving such system of random generalized variational inclusions is constructed in Banach spaces. Under some suitable conditions, we prove the convergence of the iterative sequences generated by the algorithm.

scholarly journals An iterative algorithm for generalized nonlinear variational inclusions with relaxed strongly accretive mappings in Banach spaces

2004 ◽  
Vol 2004 (20) ◽  
pp. 1035-1045 ◽  
Author(s):  
A. H. Siddiqi ◽  
Rais Ahmad
Keyword(s):  
Banach Spaces ◽  
Iterative Algorithm ◽  
Resolvent Operator ◽  
Existence Of Solutions ◽  
Operator Technique ◽  
Variational Inclusions ◽  
Special Cases ◽  
Accretive Mappings ◽  
Resolvent Operator Technique ◽  
The Resolvent Operator

We use Nadler's theorem and the resolvent operator technique form-accretive mappings to suggest an iterative algorithm for solving generalized nonlinear variational inclusions with relaxed strongly accretive mappings in Banach spaces. We prove the existence of solutions for our inclusions without compactness assumption and the convergence of the iterative sequences generated by the algorithm in real Banach spaces. Some special cases are also discussed.

scholarly journals --Accretive Mappings and a New System of Generalized Variational Inclusions with --Accretive Mappings in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Sayyedeh Zahra Nazemi
Keyword(s):  
Banach Spaces ◽  
Resolvent Operator ◽  
Lipschitz Continuity ◽  
Operator Technique ◽  
Variational Inclusions ◽  
New Class ◽  
Accretive Mappings ◽  
Resolvent Operator Technique ◽  
The Resolvent Operator ◽  
New System

We introduce a new class of generalized accretive mappings, named --accretive mappings, in Banach spaces. We define a resolvent operator associated with --accretive mappings and show its Lipschitz continuity. We also introduce and study a new system of generalized variational inclusions with --accretive mappings in Banach spaces. By using the resolvent operator technique associated with --accretive mappings, we construct a new iterative algorithm for solving this system of generalized variational inclusions in Banach spaces. We also prove the existence of solutions for the generalized variational inclusions and the convergence of iterative sequences generated by algorithm. Our results improve and generalize many known corresponding results.

scholarly journals Projection Algorithms for Variational Inclusions

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Youli Yu ◽  
Pei-Xia Yang ◽  
Khalida Inayat Noor
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Iterative Algorithm ◽  
Real Hilbert Space ◽  
Projection Algorithm ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Variational Inclusions ◽  
Projection Algorithms ◽  
Variational Inclusion Problem

We present a projection algorithm for finding a solution of a variational inclusion problem in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a solution of the variational inclusion problem which also solves some variational inequality.

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