1. A Halpern-Type Iteration Method for Bregman Nonspreading Mapping and Monotone Operators in Reflexive Banach Spaces
- Author
-
Lateef Olakunle Jolaoso, F. U. Ogbuisi, and F. O. Isiogugu
- Subjects
TheoryofComputation_MISCELLANEOUS ,Pure mathematics ,Article Subject ,Iterative method ,lcsh:Mathematics ,General Mathematics ,010102 general mathematics ,Hilbert space ,Banach space ,State (functional analysis) ,Bregman divergence ,Fixed point ,lcsh:QA1-939 ,Strongly monotone ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,ComputingMethodologies_PATTERNRECOGNITION ,Monotone polygon ,symbols ,0101 mathematics ,Mathematics - 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.
- Published
- 2019