Some fixed point results for a new three steps iteration process in Banach spaces

Abstract

Abstract. In this paper, we introduce a three step iteration method and show that this method can be used to approximate fixed point of weak contraction mappings. Furthermore, we prove that this iteration method is equivalent to Mann iterative scheme and converges faster than Picard-S iterative scheme for the class of weak contraction mappings. We also present tables and three graphics to support this result. Finally, we prove a data dependence result for weak contraction mappings using this three step iterative scheme.

A study on a new and fast fixed point iteration process in Banach spaces

“…Over the years, many researchers have efforts to develop iterative processes having faster the rate of convergence than others. In this direction, some of notable studies were conducted by Mann, Ishikawa, Noor, Suantai, Karakaya, Gursoy, Dogan, Yildirim, Karahan, Sainuan, Agarwal, Rhoades and Khan [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In addition, the fixed point mappings were studied as much as studies on the iterative methods.…”

Convergence and stability of an iterative algorithm for strongly accretive Lipschitzian operator with applications

“…The convergence and stability problems for iterative algorithms involving various types of operators have been studied by many authors [5,6,9,16,17,21,23,[26][27][28][29][30][31][32][33][34][35][36]. Nonlinear maps act as models for many systems in different scientific disciplines (see [14] for details).…”

A Hybrid Third-Order Iterative Process To Solve Nonlinear Equations

“…Over the years the interest regarding the speed of convergence of such iterations grew very fast. For example, many authors considered numerous iteration processes and studied their rate of convergence, see for details (Abbas and Nazir, 2014;Berinde, 2014;Fukhar-ud-din and Berinde, 2016;Chugh et al, 2015;Karakaya et al, 2013;Karakaya and Dogan, 2014;Dogan and Karakaya, 2018;Karakaya et al, 2017;Phuengrattana and Suantai, 2013). It is clear that the fixed point iteration methods have convergence from the first order.…”