Extending the solvability of equations using secant-type methods in Banach space


  • Ioannis K. Argyros Cameron University
  • Santhosh George Department of Mathematical and Computational Sciences, NIT Karnataka


nonlinear equations in Banach space, secant method, Secant-type method, Semi-local convergence, restricted convergence region, Lipschitz conditions


We extend the solvability of equations dened on a Banach space using numerically ecient secant-type methods. The convergence domain of these methods is enlarged using our new idea of restricted convergence region. By using this approach, we obtain a more precise location where the iterates lie than in earlier studies leading to tighter Lipschitz constants. This way the semi-local convergence produces weaker sucient convergence criteria and tighter error bounds than in earlier works. These improvements are also obtained under the same computational eort, since the new Lipschitz constants are special cases of the old ones.


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Author Biography

Ioannis K. Argyros, Cameron University

Full tenured Professor of Mathematics.


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How to Cite

Argyros, I. K., & George, S. (2021). Extending the solvability of equations using secant-type methods in Banach space. J. Numer. Anal. Approx. Theory, 50(2), 97–107. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1134