Geometrically Constructed Family of the Simple Fixed Point Iteration Method

Vinay Kanwar, Puneet Sharma, Ioannis K. Argyros, Ramandeep Behl, Christopher Argyros, Ali Ahmadian and Mehdi Salimi
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Vinay Kanwar: University Institute of Engineering and Technology, Panjab University, Chandigarh 160014, India
Puneet Sharma: University Institute of Engineering and Technology, Panjab University, Chandigarh 160014, India
Ioannis K. Argyros: Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA
Ramandeep Behl: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Christopher Argyros: Department of Computer Science, University of Oklahoma, Norman, OK 73071, USA
Ali Ahmadian: Institute of IR 4.0, The National University of Malaysia, Bangi 43600, UKM, Malaysia
Mehdi Salimi: Department of Mathematics & Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada

Mathematics, 2021, vol. 9, issue 6, 1-13

Abstract: This study presents a new one-parameter family of the well-known fixed point iteration method for solving nonlinear equations numerically. The proposed family is derived by implementing approximation through a straight line. The presence of an arbitrary parameter in the proposed family improves convergence characteristic of the simple fixed point iteration as it has a wider domain of convergence. Furthermore, we propose many two-step predictor–corrector iterative schemes for finding fixed points, which inherit the advantages of the proposed fixed point iterative schemes. Finally, several examples are given to further illustrate their efficiency.

Keywords: fixed point method; nonlinear equation; banach space; order of convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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