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Four-Step Iteration Scheme to Approximate Fixed Point for Weak Contractions

Wasfi Shatanawi1, 2, 3, *, Anwar Bataihah4, Abdalla Tallafha4
1 Department of Mathematics and General Courses, Prince Sultan University, Riyadh, 11586, Saudi Arabia.
2 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan.
3 Department of M-Commerce and Multimedia Applications, Asia University, Taichung, 41354, Taiwan.
4 Department of Mathematics, School of Science, The University of Jordan, Amman, 11942, Jordan.
* Corresponding Author: Wasfi Shatanawi. Email: .

Computers, Materials & Continua 2020, 64(3), 1491-1504. https://doi.org/10.32604/cmc.2020.010365

Received 28 February 2020; Accepted 22 April 2020; Issue published 30 June 2020

Abstract

Fixed point theory is one of the most important subjects in the setting of metric spaces since fixed point theorems can be used to determine the existence and the uniqueness of solutions of such mathematical problems. It is known that many problems in applied sciences and engineering can be formulated as functional equations. Such equations can be transferred to fixed point theorems in an easy manner. Moreover, we use the fixed point theory to prove the existence and uniqueness of solutions of such integral and differential equations. Let X be a non-empty set. A fixed point for a self-mapping T on X is a point

Keywords

Weak contraction, fixed point, iteration scheme, mean value theorem.

Cite This Article

W. Shatanawi, A. Bataihah and A. Tallafha, "Four-step iteration scheme to approximate fixed point for weak contractions," Computers, Materials & Continua, vol. 64, no.3, pp. 1491–1504, 2020.

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This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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