# Fixed Point Theory in Probabilistic Metric Spaces

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## Triangular norms in probabilistic metric spaces and fixed point theory

Usually delivered in days? Hadzic Olga. Fixed point theory in probabilistic metric spaces can be considered as a part of Probabilistic Analysis, which is a very dynamic area of mathematical research. A primary aim of this monograph is to stimulate interest among scientists and students in this fascinating field. The text is self-contained for a reader with a modest knowledge of the metric fixed point theory.

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Several themes run through this book. It follows from 4 that. Next we show the uniqueness of the fixed point. The proof is completed. Kutbi et al. In order to clearly show the content of theorem, we use a clear form to write this theorem. Then f has a fixed point. In order to get the uniqueness of fixed point, authors added the following condition:. Then f has a unique fixed point, where. This completes the proof. If the property 6 is right, then we can obtain the following result. The property 6 is right.

It is not hard to show that, the property 6 is equivalent to the following proposition. We prove the condition MPM All authors read and approved the final manuscript. Pengcheng Ma, Email: moc. Jinyu Guan, Email: moc. Yanxia Tang, Email: moc.

Yongchun Xu, Email: moc. Yongfu Su, Email: moc. National Center for Biotechnology Information , U. Published online Feb Author information Article notes Copyright and License information Disclaimer. Corresponding author. Received Nov 20; Accepted Feb Introduction and preliminaries Sometimes, it is found appropriate to assign the average of several measurements as a measure to ascertain the distance between two points.

Open question 14 Is the following property right? Conclusion 16 The property 6 is right. Competing interests The authors declare that they have no competing interests. Contributor Information Pengcheng Ma, Email: moc. References Banach S.

## Fixed Point Theory in Probabilistic Metric Spaces

Sur les oprations dans les ensembles abstraits et leur application aux quations intgrales. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Debrecen 57 , Boyd, J. Wong, On nonlinear contractions, Proc. Das, A fixed point theorem in a generalized metric space, Soochow J. Elamrani, A. Mbarki, B. Mehdaoui, Nonlinear contarctions and semigroups in general complete probabilistic metric spaces, Panamer. Palermo 22 , Gregori, A. Sapena, On fixed-point theorems in fuzzy metric spaces, Fuzzy Sets and Systems , Hadzic, A fixed point theorem in Menger spaces, Publ.

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Michalek, Fuzzy metric and statistical metric spaces, Kybernetika 11 , Kikina, K. Kikina, Fixed points on two generalized metric spaces, Int. Mbarki, A.

## Coincidence fixed point theorem in a Menger probabilistic metric spaces

Benbrik, A. Ouahab, W. Ahid, T. Menger, Statistical metrics, Proc. Bessem, A fixed point theorem in a generalized metric space for mappings satisfying a contractive condition of integral type, Int.

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Ruse 3 , Sarma, J. Rao, S. Rao, Contractions over generalized metric spaces, J. Schweizer, A. Sklar, Statistical metric spaces, Pacific J. Wald, On a statistical generalization of metric spaces, Proc. Export Citation. User Account Log in Register Help. Search Close Advanced Search Help.

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