Analyzing the semilocal convergence of a fourth-order newton-type scheme with novel majorant and average Lipschitz conditions
J.P. Jaiswal1,2,3
1Department of Mathematics, Guru Ghasidas Vishwavidyalaya, Bilaspur, India
2Faculty of Science, Barkatullah University, Bhopal,India
3Regional Institute of Education, Bhopal, India
Keywords: semilocal convergence, nonlinear problem, convergence radius, Banach space, generalized Lipschitz condition, П°-average
Abstract
The main focus of this paper is an analysis of the semilocal convergence (S.C.) of a three-step Newton-type scheme (TSNTS) used for finding the solution of nonlinear operators in Banach spaces (B.S.). A novel S.C. analysis of the TSNTS is introduced, which is based on the assumption that a generalized Lipschitz condition (G.L.C.) is satisfied by the first derivative of the operator. The findings contribute to the theoretical understanding of TSNTS in B.S. and have practical implications in various applications, such as integral equations further validating our results.
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