A New Algorithm for the Common Solutions of a Generalized Variational Inequality System and a Nonlinear Operator Equation in Banach Spaces

Yuanheng Wang, Cancan Li and Lirong Lu
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Yuanheng Wang: College of Mathematics and Computer Science, with College of Xingzhi, Zhejiang Normal University, 268 Yingbin Road, Jinhua 321004, Zhejiang, China
Cancan Li: College of Mathematics and Computer Science, with College of Xingzhi, Zhejiang Normal University, 268 Yingbin Road, Jinhua 321004, Zhejiang, China
Lirong Lu: College of Mathematics and Computer Science, with College of Xingzhi, Zhejiang Normal University, 268 Yingbin Road, Jinhua 321004, Zhejiang, China

Mathematics, 2020, vol. 8, issue 11, 1-21

Abstract: We study a new algorithm for the common solutions of a generalized variational inequality system and the fixed points of an asymptotically non-expansive mapping in Banach spaces. Under some specific assumptions imposed on the control parameters, some strong convergence theorems for the sequence generated by our new viscosity iterative scheme to approximate their common solutions are proved. As an application of our main results, we solve the standard constrained convex optimization problem. The results here generalize and improve some other authors’ recently corresponding results.

Keywords: asymptotically non-expansive mapping; general variational inequality system; strong convergence; Banach space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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