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Probabilistic b-metric spaces and nonlinear contractions [PDF]

Fixed Point Theory and Applications, 2017
This work is for giving the probabilistic aspect to the known b-metric spaces (Czerwik in Atti Semin. Mat. Fis. Univ. Modena 46(2):263-276, 1998), which leads to studying the fixed point property for nonlinear contractions in this new class of spaces.
Abderrahim Mbarki, Rachid Oubrahim
doaj   +4 more sources

Probabilistic Generalized Metric Spaces and Nonlinear Contractions

Demonstratio Mathematica, 2016
We give a probabilistic generalization of the theory of generalized metric spaces [2]. Then, we prove a fixed point theorem for a self-mapping of a probabilistic generalized metric space, satisfying the very general nonlinear contraction condition ...
Mbarki Abderrahim, Naciri Rachid
doaj   +4 more sources

Probabilistic modular metric spaces [PDF]

Journal of Hyperstructures, 2020
The purpose of this study is to investigate the connection between probabilistic and modular metric spaces. We discussseveral important properties such as convergence and completeness,etc, and the relationship among the mentioned properties in the ...
Kianoush Fathi Vajargah, Hamid Mottaghi Golshan   +1 more
doaj   +2 more sources

Fixed point theorems in metric spaces and probabilistic metric spaces [PDF]

International Journal of Mathematics and Mathematical Sciences, 1996
In this paper, we prove some common fixed point theorems for compatible mappings of type (A) in metric spaces and probabilistic metric spaces Also, we extend Caristi's fixed point theorem and Ekeland's variational principle in metric spaces to ...
Yeol Je Cho, Keun Saeng Park, Shih-Sen Chang   +2 more
doaj   +2 more sources

Probabilistic convergence spaces and generalized metric spaces [PDF]

International Journal of Mathematics and Mathematical Sciences, 1998
The category PPRS(Δ), whose objects are probabilistic pretopological spaces which satisfy an axiom (Δ) and whose morphisms are continuous mappings, is introduced.
Paul Brock
doaj   +3 more sources

Revisiting Probabilistic Metric Spaces

International Journal of Topology
The field of probabilistic metric spaces has an intrinsic interest based on a blend of ideas drawn from metric space theory and probability theory. The goal of the present paper is to introduce and study new ideas in this field.
Michael D. Rice
doaj   +2 more sources

On Weak Probabilistic φ-Contractions in Menger Probabilistic Metric Spaces

Axioms
Two new concepts are introduced in this paper: ZH-set and weak probabilistic φ-contraction. Firstly, a fixed-point theorem for weak probabilistic φ-contraction is given in Menger probabilistic metric spaces, which generalizes and unifies several results ...
Dingwei Zheng, Qingming He
doaj   +2 more sources

Strong Statistical Convergence in Probabilistic Metric Spaces

Stochastic Analysis and Applications, 2008
In this article, we introduce the concepts of strongly statistically convergent sequence and strong statistically Cauchy sequence in a probabilistic metric (PM) space endowed with the strong topology, and establish some basic facts. Next, we define the strong statistical limit points and the strong statistical cluster points of a sequence in this space
Serpil Pehlivan
exaly   +5 more sources

Generalized a-min special type contraction results on 2-Menger spaces [PDF]

Bulletin of Natural Sciences Research, 2022
The goal of this paper is to present some novel probabilistic a-minimum contraction results on probabilistic 2-metric spaces. Our findings are based on probabilistic 2-metric spaces, which are the probabilistic generalisations of 2-metric spaces.
Bhandari Samir Kumar, Chandok Sumit
doaj   +1 more source

Fixed Point Results under (ϕ, ψ)-Contractive Conditions and their Application in Optimization Problems [PDF]

Control and Optimization in Applied Mathematics, 2022
Fixed point theorems can be used to prove the solvability of optimization problems, differential equations and equilibrium problems, and the intrinsic flexibility of probabilistic metric spaces makes it possible to extend the idea of contraction mapping ...
Razieh Farokhzad Rostami
doaj   +1 more source