Bulletin of the Iranian Mathematical Society https://doi.org/10.1007/s41980-019-00260-0 ORIGINAL PAPER Iterative Approximations of Attractive Point of A New Generalized Bregman Nonspreading Mapping in Banach Spaces Bashir Ali 1 · Lawal Yusuf Haruna 1,2 Received: 16 October 2018 / Revised: 24 May 2019 / Accepted: 27 May 2019 © Iranian Mathematical Society 2019 Abstract In this paper, a generic 2-generalized Bregman nonspreading mapping is introduced. Also, a Halpern-type iterative scheme for the approximation of attractive point of such mapping is constructed in the setting of Banach space. The result established generalized some recently announced results in the literature. Keywords 2-generalized hybrid mapping · Normally 2-generalized hybrid mapping · 2-generalized nonspreading mapping · Generic generalized Bregman nonspreading mapping Mathematics Subject Classification 47H09 · 47H10 · 47J25 1 Introduction Let C be a nonempty subset of a real Hilbert space H and T : C → H be a nonlinear map. A point x ∈ H is called an attractive point of T if ‖x − Ty ‖≤‖x − y ‖ for all y ∈ C . Let the sets of attractive and fixed points of T be, respectively, denoted by A(T ) and F (T ), i.e., A(T ) ={u ∈ H :‖T v − u ‖≤‖v − u ‖, ∀v ∈ C } and F (T ) ={u ∈ C : Tu = u }. The concept of attractive point was first introduced in Hilbert space by Takahashi and Takeuchi [31]. The introduction was motivated basi- cally to get rid of the closedness and convexity hypotheses imposed on the nonempty Communicated by Ali Abkar. B Bashir Ali bashiralik@yahoo.com Lawal Yusuf Haruna yulah121@gmail.com 1 Department of Mathematical Sciences, Bayero University, Kano, Nigeria 2 Department of Mathematical Sciences, Kaduna State University, Kaduna, Nigeria 123