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In this paper, we introduce a new class of Bregman generalized <inline-formula> <math display="inline"> <semantics> <mi>&#945;</mi> </semantics> </math> </inline-formula>-nonexpansive mappings in terms of the Bregman distance. We establish several weak and strong convergence theorems of the Ishikawa and Noor iterative schemes for Bregman generalized <inline-formula> <math display="inline"> <semantics> <mi>&#945;</mi> </semantics> </math> </inline-formula>-nonexpansive mappings in Banach spaces. A numerical example is given to illustrate the main results of fixed point approximation using Halpern&#8217;s algorithm.