New generalized system of variational inclusions involving 
                
                  
                
                $$H(\cdot ,\cdot )$$
                
                  
                    
                      H
                      (
                      ·
                      ,
                      ·
                      )
                    
                  
                
              -co-accretive mapping

In this article, we consider and study a system of generalized set-valued variational inequalities involving relaxed cocoercive mappings in Hilbert spaces. Using the projection method and Banach contraction principle, we prove the existence of a solution for the considered problem. Further, we propose an iterative algorithm and discuss its convergence. Moreover, we establish equivalence between the system of variational inequalities and altering points problem. Some parallel iterative algorithms are proposed, and the strong convergence of the sequences generated by these iterative algorithms is discussed. Finally, a numerical example is constructed to illustrate the convergence analysis of the proposed parallel iterative algorithms.

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Convergence of Some Iterative Algorithms for System of Generalized Set-Valued Variational Inequalities

Akram

Khan

Dilshad

2021

Journal of Function Spaces

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New generalized system of variational inclusions involving $$H(\cdot ,\cdot )$$ H ( · , · ) -co-accretive mapping

Cited by 1 publication

References 15 publications

Convergence of Some Iterative Algorithms for System of Generalized Set-Valued Variational Inequalities

Convergence of Some Iterative Algorithms for System of Generalized Set-Valued Variational Inequalities

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