On α ̌–φ ̆-Fuzzy Contractive Mapping in Fuzzy Normed Space

Abstract

The idea of fixed points represents one of the most potent mathematical tools. This paper's main purpose is to introduce a new kind of fuzzy contractive mapping in a fuzzy normed space (briefly space) namely "fuzzy contractive mapping". We proved some fixed point results for this mapping in the setting of space using the triangular property of fuzzy norm. Moreover, under specific conditions, some other results for such type of mapping are established. Finally, an example is offered to show the results' usefulness.

Keywords

• Fixed point, F ̌_ɳ space, α ̌- admissible mapping, α ̌–φ ̆-fuzzy contractive mapping, Fuzzy Banach space.