NONLINEAR CONTRACTION MAPPING IN PROBABILISTIC CONTROLLED GENERALIZED METRIC SPACES
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Keywords:
Probabilistic controlled generalized metric spaces, Hausdorff condition, nonlinear contractions, Fixed pointAbstract
This paper presents a new framework referred to as "probabilistic
controlled generalized metric spaces," extending the theory of probabilistic metric
spaces. The aim is to examine the correlation between this innovative class and the
traditional axioms of probabilistic metric spaces. Moreover, the paper delves into
proving the existence of fixed points for the }-probabilistic contraction mapping,
even without the presence of the Hausdorff condition. The paper will also feature
illustrative examples to underscore the practicality and efficacy of the theories and
methodologies presented.
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