FIBRE CONTRACTION PRINCIPLE IN COMPLETE b-METRIC SPACES

Dedicated to the memory of Professor Mihail Megan

 

Adrian Petrușel†, Gabriela Petrușel‡, Jen-Chih Yao§

Abstract: In the framework of a complete b-metric space, we will discuss existence and uniqueness results for the fixed points of triangular operators. Using various classical metric conditions on the operators, we will obtain a generalization of the well-known fibre contraction principle in complete metric spaces.

Keywords: fixed point, complete b-metric space, contraction, Picard operator, Ulam-Hyers stability, well-posedness in the sense of Reich-Zaslavski.

MSC: 47H10, 54H25.

DOI  10.56082/annalsarscimath.2026.3.47

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*Accepted for publication on March 10, 2026
†adrian.petrusel@ubbcluj.ro, Department of Mathematics, Babeș-Bolyai University Cluj-Napoca and Academy of Romanian Scientists, 50044 Bucharest, Romania
‡gabriela.petrusel@ubbcluj.ro, Department of Business, Babeș-Bolyai University Cluj-Napoca, Romania
§yaojc@mail.cmu.edu.tw, Center for General Education, China Medical University, Taichung 404, Taiwan and Academy of Romanian Scientists, 50044 Bucharest, Romania

PUBLISHED in

Annals Academy of Romanian Scientists Series on Mathematics and Its Application,

Volume 18 no 3, 2026

ISSN ONLINE 2066 – 6594
ISSN PRINT 2066 – 5997