A Halpern-Type Iteration Method for Bregman Nonspreading Mapping and Monotone Operators in Reflexive Banach Spaces. (2nd September 2019)

• Record Type: Journal Article
• Authors: Ogbuisi, F. U.; Jolaoso, L. O.; Isiogugu, F. O.
• Other Names: Chen Jianhua Guest Editor.
• Is Part Of: Journal of mathematics. Volume 2019(2019)
• Publication Date: 2019-09-02
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2019/8059135
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : In this paper, we introduce an iterative method for approximating a common solution of monotone inclusion problem and fixed point of Bregman nonspreading mappings in a reflexive Banach space. Using the Bregman distance function, we study the composition of the resolvent of a maximal monotone operator and the antiresolvent of a Bregman inverse strongly monotone operator and introduce a Halpern-type iteration for approximating a common zero of a maximal monotone operator and a Bregman inverse strongly monotone operator which is also a fixed point of a Bregman nonspreading mapping. We further state and prove a strong convergence result using the iterative algorithm introduced. This result extends many works on finding a common solution of the monotone inclusion problem and fixed-point problem for nonlinear mappings in a real Hilbert space to a reflexive Banach space.