Generalized viscosity implicit rules for solving quasi-inclusion problems of accretive operators in Banach spaces. (3rd July 2017)

• Record Type: Journal Article
• Authors: Chang, Shih-sen; Wen, Ching-Feng; Yao, Jen-Chih
• Is Part Of: Optimization. Volume 66:Number 7(2017)
• Page Start: 1105
• Page End: 1117
• Publication Date: 2017-07-03
• Subjects: The generalized viscosity implicit rules -- accretive operator -- maximal monotone operator -- Banach space -- splitting method -- forward–backward algorithm; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1325888
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : The generalized viscosity implicit rules for solving quasi-inclusion problems of accretive operators in Banach spaces are established. The strong convergence theorems of the rules to a solution of quasi-inclusion problems of accretive operators are proved under certain assumptions imposed on the sequences of parameters. The results presented in this paper extend and improve the main results of Refs. (Moudafi, J Math Anal Appl. 2000;241:46–55; Xu et al., Fixed Point Theory Appl. 2015;2015:41; López et al., Abstr Appl Anal. 2012;2012; Cholamjiak, Numer Algor. DOI:10.1007/s11075-015-0030-6.). Moreover, some applications to monotone variational inequalities, convex minimization problem and convexly constrained linear inverse problem are presented.