DOI: 10.24193/fpt-ro.2025.1.12

Authors: Shu-Fang Li, Fei He and Shu-Min Lu

Abstract: In the framework of b-metric spaces, we establish three fixed point theorems concerning multi-valued contractions, which improve and generalize various well known results in the literature. Based on the result of Aydi et al. (Journal of Fixed Point Theory and Applications 2012: 88 2012), we give the first fixed point theorem for q-multi-valued quasi-contraction, where the range of the contraction constant is extended to Also, we establish the second result which extends the theorem presented by Haghi et al. (Applied Mathematics Letters 25: 843-846 2012) from metric spaces to b-metric spaces. Furthermore, we give a unified result to improve the recent several fixed point theorems for multi-valued mappings provided by Miculescu et al. (Journal of Fixed Point Theory an Applications 19: 2153-2163 2017). Two technical lemmas are used to ensure that a Picard sequence is a Cauchy sequence. Finally, some applications are included to vindicate that the improvements are indeed genuine.

Key Words and Phrases: Multi-valued quasi-contractions, Ćirić type contraction, Hausdorff metric, fixed point theorem.

2010 Mathematics Subject Classification: 47H10, 54H25.

Published on-line: February 1st, 2025.

Fulltext pdf

Back to volume's table of contents