Strong convergence of an inertial iterative method for generalized nonexpansive mappings in Banach spaces

We introduce an iterative technique with an inertial term that converges strongly to a fixed point of mappings satisfying Condition (E). Our results extend existing work by providing a robust numerical method for solving fixed point problems in Banach spaces. To demonstrate the effectiveness of our approach, we present numerical examples of a mapping that is not nonexpansive but satisfies Condition (E). Furthermore, we illustrate the convergence behaviour of our algorithm for different choices of initial guesses and coefficients, using MATLAB to validate the theoretical results. This work contributes to the broader framework of fixed point theory and offers practical insights for solving nonlinear problems in applied mathematics.

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