News & Announcements
Existence and Uniqueness Theorems for a Three-step Newton-type Method under $L$-Average Conditions
View Full Text  View/Add Comment  Download reader
KeyWord:Banach space; Nonlinear equation; Lipschitz condition; $L$-average; Convergence ball
Author NameAffiliation
Jai Prakash Jaiswal Department of Mathematics, Guru Ghasidas Vishwavidyalaya (A Central University), Bilaspur, C.G., India-495009
Faculty of Science, Barkatullah University, Bhopal, M.P.-462026, India
Regional Institute of Education, Bhopal, M.P.-462013, India 
Hits: 13
Download times: 17
      In this paper, we study the local convergence of a three-step Newton-type method for solving nonlinear equations in Banach spaces under weaker hypothesis. More precisely, we derive the existence and uniqueness theorems, when the first-order derivative of nonlinear operator satisfies the $L$-average conditions instead of the usual Lipschitz condition, which have been discussed in the earlier study.