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Volume 3, Issue 1, 1 April 2019, Pages 27-44
Abstract. In this paper, we first introduce the notion of the BUC property, which extends the notion of UC property introduced and studied in [T. Suzuki, M. Kikawa, C. Vetro, The existence of best proximity points in metric spaces with the property UC, Nonlinear Anal. 71 (2009), 2918-2926] for Banach spaces. We then prove, without continuity assumption on mappings, the existence and convergence of Bregman best proximity points for Bregman asymptotic cyclic contractions in Banach spaces with the property BUC and Bregman asymptotic proximal pointwise contractions in uniformly convex Banach spaces. Moreover, we consider a Bregman generalized cyclic contraction mapping and prove the existence of Bregman best proximity points for such a mapping in Banach spaces which do not necessarily satisfy the geometric property BUC.
How to Cite this Article:
Eskandar Naraghirad, Bregman best proximity points for Bregman asymptotic cyclic contraction mappings in Banach spaces, J. Nonlinear Var. Anal. 3 (2019), 27-44.