TY - JOUR
AU - Ogbuisi, F. U.
AU - Jolaoso, L. O.
AU - Isiogugu, F. O.
PY - 2019
DA - 2019/09/02
TI - A Halpern-Type Iteration Method for Bregman Nonspreading Mapping and Monotone Operators in Reflexive Banach Spaces
SP - 8059135
VL - 2019
AB - 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.
SN - 2314-4629
UR - https://doi.org/10.1155/2019/8059135
DO - 10.1155/2019/8059135
JF - Journal of Mathematics
PB - Hindawi
KW -
ER -