Abstract
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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This work is supported by King Mongkut’s Institute of Technology Ladkrabang.
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Chaloemyotphong, B., Kangtunyakarn, A. A theorem for solving Banach generalized system of variational inequality problems and fixed point problem in uniformly convex and 2-uniformly smooth Banach space. RACSAM 115, 93 (2021). https://doi.org/10.1007/s13398-021-01036-0
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DOI: https://doi.org/10.1007/s13398-021-01036-0