ON BANACH'S FIXED POINT THEOREM IN PERTURBED METRIC SPACES
Mohamed Jleli, Bessem Samet
Abstract
The measurement of the distance between two points is always tainted by errors. The causes of such errors are varied. For instance, the imperfection in the adjustment of instruments affects the accuracy of measurements. These errors are generally "small", however their accumulations can become significant. Motivated by this fact, in this paper, we introduce the notion of perturbed metric spaces and establish an interesting generalization of Banach's fixed point theorem in such spaces.
Topics & Concepts
Fixed-point theoremMathematicsEberlein–Šmulian theoremBanach spaceMetric spaceFixed pointBanach fixed-point theoremPure mathematicsMathematical analysisLp spaceDifferential Equations and Numerical MethodsFixed Point Theorems Analysis