A theorem for solving Banach generalized system of variational inequality problems and fixed point problem in uniformly convex and 2-uniformly smooth Banach space

被引：0
作者：
Bunyawee Chaloemyotphong
Atid Kangtunyakarn
机构：
[1] King Mongkut’s Institute of Technology Ladkrabang,Department of Mathematics, Faculty of Science
来源：
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas | 2021年 / 115卷
关键词：
Fixed point problem; Nonexpansive mapping; Variational inequality problem; 47H10; 47H07; 47J30;
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摘要：
In this paper, we consider a Banach generalized system of variational inequality problems by using the concept of Kangtunyakarn (Fixed Point Theory Appl 2014:123, 2014) and showed the equivalence between a Banach generalized system of variational inequality problems and fixed point problems. And also, using modified viscosity iterative method, we prove a strong convergence theorem for finding a common solution of a Banach generalized system of variational inequality problems and fixed point problems for a nonexpansive mapping. The main theorem presented in this paper extend the corresponding result of variational inequality problems introduced by Aoyama et al. (Fixed Point Theory Appl 2006:35390, https://doi.org/10.1155/FPTA/2006/35390, 2006). Moreover, we give some numerical examples for supporting our main theorem.
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