A Convergence Analysis for Secant-like Methods with Applications to Fractional Calculus

摘要

We present local and semilocal convergence results for secant-like methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. In the last part of the study we present some choices of the operators involved in fractional calculus where the operators satisfy the convergence conditions. AMS Subject Classification: 65G99, 65H10, 26A33, 47J25, 47J05