A Halpern-Type Iteration Method for Bregman Nonspreading Mapping and Monotone Operators in Reflexive Banach Spaces

F. U. Ogbuisi*, L. O. Jolaoso, F. O. Isiogugu, Jianhua Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number8059135
JournalJournal of Mathematics
Volume2019
DOIs
Publication statusPublished - 2019
Externally publishedYes

Fingerprint

Dive into the research topics of 'A Halpern-Type Iteration Method for Bregman Nonspreading Mapping and Monotone Operators in Reflexive Banach Spaces'. Together they form a unique fingerprint.

Cite this