Common Attractive Point Approximations for Family of Generic Generalized Bregman Nonspreading Mappings in Banach Spaces

In this paper, a class of generic generalized Bregman nonspreading mappings which is said to include the classes of generalized Bregman nonspreading, generic generalized nonspreading, generalized hybrid mappings etc. as special cases is investigated. Then, a theorem for existence of attractive point of the said mapping is established in the setting of reflexive Banach spaces. Also, we prove a demiclosedness property and construct a Halpern type iterative algorithm that converges strongly to the common attractive point of finite family of generic generalized Bregman nonspreading mappings in the space. We further apply our main result to approximate common fixed point of the said mappings. Our results improve and generalize many corresponding ones announced in the literature.