On modified proximal point algorithms for solving minimization problems and fixed point problems in CAT(κ) spaces. (6th November 2019)

• Record Type: Journal Article
• Authors: Pakkaranang, Nuttapol; Kumam, Poom; Wen, Ching‐Feng; Yao, Jen‐Chih; Cho, Yeol Je
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 17(2021)
• Page Start: 12369
• Page End: 12382
• Publication Date: 2019-11-06
• Subjects: CAT(1) spaces -- minimization problem -- nonexpansive mapping -- proximal point algorithm -- resolvent operator; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5965
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we show the existence of solutions of the convex minimization problems and common fixed problems in CAT(1) spaces under some mild conditions. For this, we propose the new modified the proximal point algorithm. Further, we give some applications for the convex minimization problem and the fixed point problem in CAT( κ ) spaces with the bounded positive real number κ . Our results improve and generalize many recent important results in the literature.