On φ-contractions and fixed point results in fuzzy metric spaces

Abstract

In this paper, φ-contractions are defined and then, some new fixed point theorems are established for certain nonlinear mappings associated with one-dimensional (c)-comparison functions in fuzzy metric spaces. Next, generalized φ-contractions are defined by using five-dimensional (c)-comparison functions, and the existence of fixed points for nonlinear maps on fuzzy metric spaces is studied. Moreover, some examples are given to illustrate our results.

Keywords

• φ-contraction
• weak φ-contraction
• fuzzy metric space
• multiple fixed point
• comparison function