On some fixed point results using [Formula: see text] simulation functions via w-distance with applications

Said Atallaoui; Fady Hasan; Wasfi Shatanawi; Zead Mustafa; Abdalla Tallafha

doi:10.1016/j.heliyon.2024.e29345

On some fixed point results using $C_{G}$ simulation functions via w-distance with applications

Heliyon. 2024 Apr 10;10(8):e29345. doi: 10.1016/j.heliyon.2024.e29345. eCollection 2024 Apr 30.

Authors

Said Atallaoui¹, Fady Hasan², Wasfi Shatanawi^{2

3

4}, Zead Mustafa⁴, Abdalla Tallafha⁵

Affiliations

¹ Department of Mathematics, Ziane Achour University, Djelfa 17000, Algeria.
² Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia.
³ Department of Medical Research, China Medical University, Taichung 40402, Taiwan.
⁴ Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa 13133, Jordan.
⁵ Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan.

Abstract

Based on the notion of class of $C_{G}$ simulation functions, we launch the concept of $(ρ, ϑ)$ - $Z_{G}$ -contraction on the setting of w-distance mappings. We employ our new concept to formulate and prove several fixed point results over the complete metric spaces. Also, we provide some concrete examples to show the usability of the obtained results. Furthermore, we study the existence of a unique solution of nonlinear fractional differential equations, nonlinear integral equations and spring-mass system problems. The results presented in this manuscript generalize many of the results known in the literature.

Keywords: $(ρ, ϑ)$ - $Z_{G}$ -contraction; $C_{G}$ simulation functions; Fixed point; w-distance mappings.