TY - JOUR
T1 - ON SPLIT EQUALITY MONOTONE VARIATIONAL INCLUSION AND FIXED POINT PROBLEMS IN REFLEXIVE BANACH SPACES
AU - Abass, Hammed Anuoluwapo
AU - Oyewole, Olawale Kazeem
AU - Aphane, Maggie
N1 - Publisher Copyright:
© 2024 Juliusz Schauder Centre for Nonlinear Studies Nicolaus Copernicus University in Toruń.
PY - 2024/9
Y1 - 2024/9
N2 - In this paper, motivated by the works of Akbar and Shahros-vand [Filomat 32 (2018), no. 11, 3917–3932], Ogbuisi and Izuchukwu [Nu-mer. Funct. Anal. Optim. 41 (2020), no. 2, 322–343], and some other related results in the literature, we introduce a Halpern iterative algorithm and employ a Bregman distance approach for approximating a solution of split equality monotone variational inclusion problem and fixed point problem of Bregman relatively nonexpansive mapping in reflexive Banach spaces. Under suitable condition, we state and prove a strong convergence result for approximating a common solution of the aforementioned prob-lems. Furthermore, we give an application of our main result to variational inequality problems and provide some numerical examples to illustrate the convergence behavior of our result. The result presented in this paper ex-tends and complements many related results in literature.
AB - In this paper, motivated by the works of Akbar and Shahros-vand [Filomat 32 (2018), no. 11, 3917–3932], Ogbuisi and Izuchukwu [Nu-mer. Funct. Anal. Optim. 41 (2020), no. 2, 322–343], and some other related results in the literature, we introduce a Halpern iterative algorithm and employ a Bregman distance approach for approximating a solution of split equality monotone variational inclusion problem and fixed point problem of Bregman relatively nonexpansive mapping in reflexive Banach spaces. Under suitable condition, we state and prove a strong convergence result for approximating a common solution of the aforementioned prob-lems. Furthermore, we give an application of our main result to variational inequality problems and provide some numerical examples to illustrate the convergence behavior of our result. The result presented in this paper ex-tends and complements many related results in literature.
KW - Bregman relatively nonexpansive map-pings
KW - Split equality problem
KW - fixed point problem
KW - iterative scheme
KW - monotone operators
UR - http://www.scopus.com/inward/record.url?scp=85209122988&partnerID=8YFLogxK
U2 - 10.12775/TMNA.2024.009
DO - 10.12775/TMNA.2024.009
M3 - Article
AN - SCOPUS:85209122988
SN - 1230-3429
VL - 64
SP - 317
EP - 338
JO - Topological Methods in Nonlinear Analysis
JF - Topological Methods in Nonlinear Analysis
IS - 1
ER -