EXTENDED FOUR PARAMETER CHEBYSHEV-HALLEY-TYPE METHODS OF ORDER SIX

Abstract: A study of the local and the semilocal convergence is carried out for the Chebyshev-Halley-type iterative methods under ω-type conditions. The conditions are imposed only on the first-order derivatives. In both cases, the convergence region and the region of uniqueness of the solution is established. The new technique is a usefull alternative to expensive Taylor series used to study the convergence of iterative methods requiring high order derivatives not on the methods. The results of a numerical experiment are presented to check the convergence conditions.

Keywords: complete normed space, Chebyshev-Halley-type methods, local and semi-local convergence, order six.

MSC: 65J15, 65H10, 65G99, 47H30.

DOI       10.56082/annalsarscimath.2026.2.111

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^†iargyros@cameron.edu, Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
^‡stepa.shakhno@lnu.edu.ua, Department of Theory of Optimal Processes, Ivan Franko National University of Lviv, Lviv, Ukraine
^§halyna.yarmola@lnu.edu.ua, Department of Computational Mathematics, Ivan Franko National University of Lviv, Lviv, Ukraine

PUBLISHED in

Annals Academy of Romanian Scientists Series on Mathematics and Its Application,

Volume 18 no 2, 2026

ISSN ONLINE 2066 – 6594
ISSN PRINT 2066 – 5997