A system of generalized variational inclusions involving generalized H(·,·)-accretive mapping in real q-uniformly smooth Banach spaces

2011 ◽  
Vol 217 (23) ◽  
pp. 9679-9688 ◽  
Author(s):  
K.R. Kazmi ◽  
F.A. Khan ◽  
Mohammad Shahzad
Keyword(s):  
Banach Spaces ◽  
Variational Inclusions ◽  
Accretive Mapping ◽  
Uniformly Smooth ◽  
Uniformly Smooth Banach Spaces

scholarly journals System of Multi-Valued Mixed Variational Inclusions with XOR-Operation in Real Ordered Uniformly Smooth Banach Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1027
Author(s):  
Rais Ahmad ◽  
Imran Ali ◽  
Xiao-Bing Li ◽  
Mohd. Ishtyak ◽  
Ching-Feng Wen
Keyword(s):  
Banach Spaces ◽  
Iterative Algorithm ◽  
Convergence Result ◽  
Variational Inclusions ◽  
Uniformly Smooth ◽  
Xor Operation ◽  
Uniformly Smooth Banach Spaces

In this paper, we consider and study a system of multi-valued mixed variational inclusions with XOR-operation ⊕ in real ordered uniformly smooth Banach spaces. This system consists of bimappings, multi-valued mappings and Cayley operators. An iterative algorithm is suggested to find the solution to a system of multi-valued mixed variational inclusions with XOR-operation ⊕ and consequently an existence and convergence result is proved. In support of our main result, an example is constructed.

scholarly journals Algorithms for General System of Generalized Resolvent Equations with Corresponding System of Variational Inclusions

2012 ◽  
Vol 2012 ◽  
pp. 1-24
Author(s):  
Lu-Chuan Ceng ◽  
Ching-Feng Wen
Keyword(s):  
Banach Spaces ◽  
General System ◽  
Approximate Solutions ◽  
Variational Inclusions ◽  
Convergence Criteria ◽  
Generalized Resolvent ◽  
Resolvent Equations ◽  
Uniformly Smooth ◽  
Uniformly Smooth Banach Spaces ◽  
Generalized Resolvent Equations

Very recently, Ahmad and Yao (2009) introduced and considered a system of generalized resolvent equations with corresponding system of variational inclusions in uniformly smooth Banach spaces. In this paper we introduce and study a general system of generalized resolvent equations with corresponding general system of variational inclusions in uniformly smooth Banach spaces. We establish an equivalence relation between general system of generalized resolvent equations and general system of variational inclusions. The iterative algorithms for finding the approximate solutions of general system of generalized resolvent equations are proposed. The convergence criteria of approximate solutions of general system of generalized resolvent equations obtained by the proposed iterative algorithm are also presented. Our results represent the generalization, improvement, supplement, and development of Ahmad and Yao corresponding ones.

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