scholarly journals Convergence and stability of iterative algorithm for a new system of (A,η)-accretive mapping inclusions in Banach spaces

2008 ◽  
Vol 56 (9) ◽  
pp. 2305-2311 ◽  
Author(s):  
Mao-Ming Jin
Keyword(s):  
Banach Spaces ◽  
Iterative Algorithm ◽  
Accretive Mapping ◽  
Convergence And Stability ◽  
New System

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 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.

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