A Study on Fixed-Point Techniques under the <i>α</i>-<i>ϝ</i>-Convex Contraction with an Application
Gunasekaran Nallaselli,
Arul Joseph Gnanaprakasam,
Gunaseelan Mani,
Ozgur Ege,
Dania Santina,
Nabil Mlaiki
Affiliations
Gunasekaran Nallaselli
Department of Mathematics, College of Engineering and Technology, Faculty of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur 603203, Tamil Nadu, India
Arul Joseph Gnanaprakasam
Department of Mathematics, College of Engineering and Technology, Faculty of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur 603203, Tamil Nadu, India
Gunaseelan Mani
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, Tamil Nadu, India
Ozgur Ege
Department of Mathematics, Ege University, Bornova, 35100 Izmir, Turkey
Dania Santina
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Nabil Mlaiki
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
In this paper, we consider several classes of mappings related to the class of α-ϝ-contraction mappings by introducing a convexity condition and establish some fixed-point theorems for such mappings in complete metric spaces. The present result extends and generalizes the well-known results of α-admissible and convex contraction mapping and many others in the existing literature. An illustrative example is also provided to exhibit the utility of our main results. Finally, we derive the existence and uniqueness of a solution to an integral equation to support our main result and give a numerical example to validate the application of our obtained results.
