Algorithm for solving a new class of generalized nonlinear implicit quasi-variational inclusions in Banach spaces

2009 ◽  
Vol 208 (2) ◽  
pp. 547-555 ◽  
Author(s):  
Xie Ping Ding ◽  
Hai Rong Feng
Keyword(s):  
Banach Spaces ◽  
Variational Inclusions ◽  
New Class

scholarly journals Noor Iterative Approximation for Solutions to Variational Inclusions with k-Subaccretive Type Mappings in Reflexive Banach Spaces

2012 ◽  
Vol 20 (1) ◽  
pp. 505-517
Author(s):  
Shuyi Zhang ◽  
Xinqi Guo ◽  
Jun Wang
Keyword(s):  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Variational Inclusions ◽  
Reflexive Banach Spaces ◽  
Iterative Approximation ◽  
Inclusion Problems ◽  
Convergence And Stability ◽  
New Class ◽  
Conver Gence

Abstract In this paper, we introduce and study a new class of nonlinear vari- ational inclusion problems with Lipschitz k-subaccretive type mappings in real reflexive Banach spaces. The existence and uniqueness of such solutions are proved and the convergence and stability of Noor iterative sequences with errors are also discussed. Furthermore, general conver- gence rate estimates are given in our results, which essentially improve and extend the corresponding results in Chang[1, 2], Ding[3], Gu[5, 6, 7], Hassouni andMoudafi[8], Kazmi[9], Noor[11, 12], Siddiqi and Ansari[13], Siddiqi, Ansari and Kazmi[14] and Zeng[16].

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.

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