Fixed point theorems for Bregman hybrid multivalued mappings with applications in Banach spaces
Fixed Point Methods and Optimization, Volume 2, Issue 3, December 2025, Pages 167–197
DEBDULAL GHOSH
School of Applied Sciences (Mathematics), KIIT University, Campus-3 (Kathajori Campus), Bhubaneswar 751024, Odisha, India
YEKINI SHEHU
School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, People’s Republic of China
ESKANDAR NARAGHIRAD
Department of Mathematics, Yasouj University, Yasouj 75918, Iran
Abstract
In the present article, we introduce a new class of mappings called Bregman hybrid multivalued mappings in Banach spaces. We then prove fixed points theorems for these mappings. Further, in the absence of the Opial property of Banach spaces, we provide a variety of weak and strong convergence theorems for a finite family of the above-mentioned mappings. We continue investigating the equilibrium problems by applying our results to nonlinear bifunctions. Since the Bregman distance has no symmetric property and does not require triangle inequality, the improved results can be considered as unifications of the corresponding ones in the literature.
Cite this Article as
Debdulal Ghosh, Yekini Shehu and Eskandar Naraghirad, Fixed point theorems for Bregman hybrid multivalued mappings with applications in Banach spaces, Fixed Point Methods and Optimization, 2(3), 167–197, 2025