A hybrid shrinking projection method for common fixed points of a finite family of demicontractive mappings with variational inequality problems

• Main Authors: Suthep Suantai, Withun Phuengrattana
• Format: Journal
• Published: 2018
• Subjects: Mathematics
• Online Access: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85024865473&origin=inward; http://cmuir.cmu.ac.th/jspui/handle/6653943832/57512
• Institution: Chiang Mai University

© 2017 by the Tusi Mathematical Research Group. In this article, we prove some properties of a demicontractive mapping defined on a nonempty closed convex subset of a Hilbert space. By using these properties, we obtain strong convergence theorems of a hybrid shrinking projection method for finding a common element of the set of common fixed points of a finite family of demicontractive mappings and the set of com- mon solutions of a finite family of variational inequality problems in a Hilbert space. A numerical example is presented to illustrate the proposed method and convergence result. Our results improve and extend the corresponding results existing in the literature.