Fixed-Point Theorems in Fuzzy Metric Spaces via Fuzzy F-Contraction
Huaping Huang, Biljana Carić, Tatjana Došenović, Dušan Rakić, Mirjana Brdar
Abstract
The purpose of this paper is to introduce a new type of contraction called fuzzy F-contraction. As compared to the F-contraction in the existing literature, our fuzzy F-contraction is much simpler and more straightforward, since it contains only one condition—that is, the function F is strictly increasing. Moreover, some fixed-point theorems for fuzzy F-contraction are presented. Further, some examples are given to illustrate its validity and superiority. In addition, by applying a very significant lemma, we show that our proofs of most fixed-point theorems are shorter and more elegant than ones in the literature.
Topics & Concepts
Contraction (grammar)MathematicsMathematical proofFuzzy logicFixed pointContraction mappingLemma (botany)Discrete mathematicsPure mathematicsFixed-point theoremMathematical analysisComputer scienceArtificial intelligenceGeometryLinguisticsEcologyBiologyPoaceaePhilosophyFixed Point Theorems Analysis