Strong convergence theorem by shrinking projection method for new nonlinear mappings in Banach spaces and applications. (3rd April 2017)

• Record Type: Journal Article
• Authors: Takahashi, Wataru; Wen, Ching-Feng; Yao, Jen-Chih
• Is Part Of: Optimization. Volume 66:Number 4(2017)
• Page Start: 609
• Page End: 621
• Publication Date: 2017-04-03
• Subjects: Fixed point -- generalized projection -- generalized resolvent -- shrinking projection method -- duality mappinng; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1276180
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: In this paper, we introduce the concept of a new nonlinear mapping called demigeneralized in a Banach space. Then, using the shrinking projection method, we prove a strong convergence theorem for finding a common fixed point for a family of the new nonlinear mappings in a Banach space. We apply this result to obtain new strong convergence theorems in a Hilbert space and a Banach space, respectively.