Document Type : Research Paper

Authors

• Arslan Hojat Ansari ¹
• Bahman Moeini ²
• Isa Yildirim ³
• Anca Maria Oprea ⁴

¹ Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

² Department of Mathematics, Hidaj Branch, Islamic Azad University, Hidaj, Iran

³ Department of Mathematics, Faculty of Science, Ataturk University, 25240 Erzurum, Turkey

⁴ Babe s-Bolyai University, Faculty of Mathematics and Computer Sciences, 400084 Cluj-Napoca, Romania

Abstract

In this paper, by using C-class functions, we will present a coupled fixed problem in b-metric space for the single-valued operators satisfying a generalized contraction condition. The first part of the paper is related to some fixed point theorems, the second part presents the uniqueness and existence of the solution of the coupled fixed point problem and in the third part, we discuss data dependence, well-posedness, Ulam-Hyers stability and limit shadowing property of the coupled fixed point set.

Keywords

• Fixed point
• ordered metric space
• rational type contraction
• coupled fixed point
• data dependence
• well-posedness
• Ulam-Hyers stability
• limit shadowing property