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Attractive point and nonlinear ergodic theorems without convexity in reflexive Banach spaces

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Abstract

In this paper, we prove attractive point theorem for two commutative generic 2-generalized Bregman nonspreading mappings in reflexive Banach spaces. Also, a nonlinear ergodic theorem of Baillon type without convexity assumption on the aforementioned mappings is proved in the space. Our results improve and generalize many results announced recently in the literature.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Bayero University, Kano, Nigeria

    Bashir Ali

  2. Department of Mathematical Sciences, Kaduna State University, Kaduna, Nigeria

    Lawal Yusuf Haruna

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  1. Bashir Ali
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  2. Lawal Yusuf Haruna
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Correspondence to Bashir Ali.

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Ali, B., Haruna, L.Y. Attractive point and nonlinear ergodic theorems without convexity in reflexive Banach spaces. Rend. Circ. Mat. Palermo, II. Ser 70, 1527–1540 (2021). https://doi.org/10.1007/s12215-020-00574-7

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  • DOI: https://doi.org/10.1007/s12215-020-00574-7

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