| Summary: | In this paper, we consider a faster iterative method for approximating the fixed points of generalized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-nonexpansive mappings. We prove several weak and strong convergence theorems of the considered method in mild conditions within the control parameters. In order to validate our findings, we present some nontrivial examples of the considered mappings. Furthermore, we show that the class of mappings considered is more general than some nonexpansive-type mappings. Also, we show numerically that the method studied in our article is more efficient than several existing methods. Lastly, we use our main results to approximate the solution of a delay fractional differential equation in the Caputo sense. Our results generalize and improve many well-known existing results.
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