New Fuzzy Fixed Point Results in Generalized Fuzzy Metric Spaces With Application to Integral Equations
Muhammad Sohail Ashraf, Rashid Ali, Nawab Hussain
Abstract
In this paper, we introduce the notion of generalized fuzzy metric space. Many topological spaces like fuzzy metric spaces, fuzzy b-metric spaces and dislocated fuzzy metric spaces have been generalized by this new generalized fuzzy metric space. We prove the Banach contraction principle and Ćirić's quasi-contraction theorem in the setting of generalized fuzzy metric space and furnish an example to illustrate our results. As consequences of our results we obtain Jleli and Samet and many other authors recent results as corollaries. An application related to our main result for nonlinear integral equation is also presented.
Topics & Concepts
MathematicsMetric spaceT-normFuzzy logicInjective metric spaceContraction principleConvex metric spaceMetric (unit)Pure mathematicsFixed-point theoremContraction (grammar)Intrinsic metricProduct metricDiscrete mathematicsMathematical analysisApplied mathematicsFuzzy numberFuzzy setComputer scienceArtificial intelligenceOperations managementInternal medicineMedicineEconomicsFixed Point Theorems Analysis