DOI: 10.24193/fpt-ro.2026.2.15

Authors: M.A. Hernández-Verón, Sukhjit Singh, Eulalia Martínez, Sonia Yadav

Abstract: In this study, we introduce a new result based on auxiliary points to establish the domains of global convergence for Secant method. We assume generalized conditions on divided difference operator that cover differential as well as non-differentiable operators. In addition, we obtain semilocal and local convergence results as a particular case. Moreover, we implement our theoretical results on nonlinear integral Hammerstein type equations to show the applicability of our work. Furthermore, we have obtained a new fixed point result by using the Secant method.

Key Words and Phrases: Secant method, recurrence relations, global convergence, convergence balls, integral equations

2020 Mathematics Subject Classification: 65H10, 65J15, 45G10, 47H10, 47H99.

Published on-line: June 1st, 2026.

Fulltext pdf

Back to volume's table of contents