Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Proving Fixed Point Theorems Employing Fuzzy $(\sigma,\mathcal{Z})$-Contractive Type Mappings

Version 1 : Received: 31 August 2021 / Approved: 1 September 2021 / Online: 1 September 2021 (09:21:14 CEST)

How to cite: Saleh, H.N.; Imdad, M.; Sessa, S.; Di Martino, F. Proving Fixed Point Theorems Employing Fuzzy $(\sigma,\mathcal{Z})$-Contractive Type Mappings. Preprints 2021, 2021080577 (doi: 10.20944/preprints202108.0577.v1). Saleh, H.N.; Imdad, M.; Sessa, S.; Di Martino, F. Proving Fixed Point Theorems Employing Fuzzy $(\sigma,\mathcal{Z})$-Contractive Type Mappings. Preprints 2021, 2021080577 (doi: 10.20944/preprints202108.0577.v1).

## Abstract

In this article, the concept of fuzzy $(\sigma,\mathcal{Z})$-contractive mapping has been introduced in fuzzy metric spaces which is an improvement over the corresponding concept recently introduced by Shukla et al. [Fuzzy Sets and system. 350 (2018) 85--94]. Thereafter, we utilized our newly introduced concept to prove some existence and uniqueness theorems in $\mathcal{M}$-complete fuzzy metric spaces. Our results extend and generalize the corresponding results of Shukla et al.. Moreover, an example is adopted to exhibit the utility of newly obtained results.

## Keywords

fuzzy $(\sigma,\mathcal{Z})$-contractive mappings; fuzzy metric spaces; fuzzy-$\mathcal{Z}$-contractive mappings}

## Subject

MATHEMATICS & COMPUTER SCIENCE, Analysis

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