TY - JOUR
T1 - An iterative method for solving minimization, variational inequality and fixed point problems in reflexive Banach spaces
AU - Jolaoso, Lateef Olakunle
AU - Ogbuisi, Ferdinard Udochukwu
AU - Mewomo, Oluwatosin Temitope
N1 - Funding Information:
The second author acknowledges thankfully the bursary and fnancial support from Department of Science and Technology and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DST-NRF COE-MaSS) Doctoral Bursary. Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the CoE-MaSS.
Publisher Copyright:
© 2018 Walter de Gruyter GmbH, Berlin/Boston.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - In this paper, we propose an iterative algorithm for approximating a common fixed point of an infinite family of quasi-Bregman nonexpansive mappings which is also a solution to finite systems of convex minimization problems and variational inequality problems in real reflexive Banach spaces. We obtain a strong convergence result and give applications of our result to finding zeroes of an infinite family of Bregman inverse strongly monotone operators and a finite system of equilibrium problems in real reflexive Banach spaces. Our result extends many recent corresponding results in literature.
AB - In this paper, we propose an iterative algorithm for approximating a common fixed point of an infinite family of quasi-Bregman nonexpansive mappings which is also a solution to finite systems of convex minimization problems and variational inequality problems in real reflexive Banach spaces. We obtain a strong convergence result and give applications of our result to finding zeroes of an infinite family of Bregman inverse strongly monotone operators and a finite system of equilibrium problems in real reflexive Banach spaces. Our result extends many recent corresponding results in literature.
KW - Bregman distance
KW - Bregman projection
KW - Fréchet differentiable functions
KW - Gâteaux differentiable function
KW - Legendre functions
KW - convex minimization problem
KW - reffexive Banach space
KW - resolvent
KW - strong convergence
KW - variational inequality
UR - http://www.scopus.com/inward/record.url?scp=85040225264&partnerID=8YFLogxK
U2 - 10.1515/apam-2017-0037
DO - 10.1515/apam-2017-0037
M3 - Article
AN - SCOPUS:85040225264
VL - 9
SP - 167
EP - 184
JO - Advances in Pure and Applied Mathematics
JF - Advances in Pure and Applied Mathematics
SN - 1867-1152
IS - 3
ER -