title: Semilocal convergence theorem for the inverse-free Jarratt method under new Hölder conditions.
abstract: Under the new Hölder conditions, we consider the convergence analysis of the inverse-free Jarratt method in Banach space which is used to solve the nonlinear operator equation. We establish a new semilocal convergence theorem for the inverse-free Jarratt method and present an error estimate. Finally, three examples are provided to show the application of the theorem.
authors.affiliation: Department of Mathematics, Taizhou University, Linhai, Zhejiang 317000, China.
authors.forename: Yueqing
authors.initials: Y
authors.lastname: Zhao
authors.affiliation: Department of Mathematics, Taizhou University, Linhai, Zhejiang 317000, China.
authors.forename: Rongfei
authors.initials: R
authors.lastname: Lin
authors.affiliation: Department of Mathematics, Brno University of Technology, 616 00 Brno, Czech Republic.
authors.forename: Zdenek
authors.initials: Z
authors.lastname: Šmarda
authors.affiliation: Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, China.
authors.forename: Yasir
authors.initials: Y
authors.lastname: Khan
authors.affiliation: Department of Mathematics, Taizhou University, Linhai, Zhejiang 317000, China.
authors.forename: Jinbiao
authors.initials: J
authors.lastname: Chen
authors.affiliation: Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, China.
authors.forename: Qingbiao
authors.initials: Q
authors.lastname: Wu