Fixed point results in fuzzy metric spaces via α and β_κ–admissible mappings with application to integral types

Article type: Research Article

Authors: Phiangsungnoen, Supak^a | Thounthong, Phatiphat^b | Kumam, Poom^{c; d; e; *}

Affiliations: [a] Department of Mathematics, Faculty of Liberal Arts, Rajamangala University of Technology Rattanakosin (RMUTR), Chakkrawat, Samphanthawong, Bangkok, Thailand | [b] Renewable Energy Research Centre and Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok, Thailand | [c] KMUTT-Fixed Point Research Laboratory, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thung Khru, Bangkok, Thailand | [d] KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thung Khru, Bangkok, Thailand | [e] Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

Correspondence: [*] Corresponding author. Poom Kumam. E-mails: poom.kum@kmutt.ac.th; poom.kumam@mail.kmutt.ac.th.

Abstract: In this paper, we introduce and prove some classes of fuzzy contractive mappings with altering distance function via α and βκ–admissible mappings in the fuzzy metric spaces. We also give some example and graph which demonstrate the validity of the hypotheses of our main results. Our results improve and extend several previously known fixed point theorems of the existing literature. As an application to our main result a fixed point for contraction mappings of integral type in fuzzy metric spaces are presented.

Keywords: α-admissible mapping, altering distance, β_κ–admissible mapping, fixed point, fuzzy metric spaces

DOI: 10.3233/JIFS-17350

Journal: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 1, pp. 467-475, 2018