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In this paper, we introduce a new class of Bregman generalized$\alpha$-nonexpansive mappings in terms of Bregman distances, and investigatethe Ishikawa and Noor iterations for these mappings. We establish weak andstrong convergence theorems of Ishikawa and Noor iterative schemes for Bregmangeneralized $\alpha$-nonexpansive mappings in Banach spaces. Furthermore, wepropose an example of our generated mapping and some numerical examples whichsupport our main theorem. Our results are new and improve the recent ones inthe literature.

Approximating Fixed points of Bregman Generalized $\alpha$-nonexpansive mappings