Ćirić-Type Operators and Common Fixed Point Theorems

Claudia Luminiţa Mihiţ, Ghiocel Moţ and Gabriela Petruşel
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Claudia Luminiţa Mihiţ: Department of Mathematics and Computer Science, “Aurel Vlaicu” University of Arad, Elena Drăgoi Street no. 2, 310330 Arad, Romania
Ghiocel Moţ: Department of Mathematics and Computer Science, “Aurel Vlaicu” University of Arad, Elena Drăgoi Street no. 2, 310330 Arad, Romania
Gabriela Petruşel: Department of Business, Babeş-Bolyai University Cluj-Napoca, Horea Street no. 7, 400174 Cluj-Napoca, Romania

Mathematics, 2022, vol. 10, issue 11, 1-9

Abstract: In the context of a complete metric space, we will consider the common fixed point problem for two self operators. The operators are assumed to satisfy a general contraction type condition inspired by the Ćirić fixed point theorems. Under some appropriate conditions we establish existence, uniqueness and approximation results for the common fixed point. In the same framework, the second problem is to study various stability properties. More precisely, we will obtain sufficient conditions assuring that the common fixed point problem is well-posed and has the Ulam–Hyers stability, as well as the Ostrowski property for the considered problem. Some examples and applications are finally given in order to illustrate the abstract theorems proposed in the first part of the paper. Our results extend and complement some theorems in the recent literature.

Keywords: metric space; fixed point; common fixed point; pair of ?iri?-type operators; well-posedness; Ulam–Hyers stability; Ostrowski property (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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