Fixed point results for cyclic contractions in Menger PM-spaces and generalized Menger PM-spaces

Fixed point results for cyclic contractions in Menger PM-spaces and generalized Menger PM-spaces In this paper, we introduce the concepts of cyclic $$\varphi $$ φ -contractions in Menger PM-spaces and cyclic weak $$\phi $$ ϕ -contractions in generalized Menger PM-spaces. Based on these concepts, some fixed point results for cyclic $$\varphi $$ φ -contractions in Menger PM-spaces are obtained. Furthermore, some fixed point theorems for cyclic weak $$\phi $$ ϕ -contractions and cyclic $$\varphi $$ φ -contractions in generalized Menger PM-spaces are obtained by assuming that the number of cyclic sets is odd. An example is also given to show the validity of our main results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Springer Journals

Fixed point results for cyclic contractions in Menger PM-spaces and generalized Menger PM-spaces

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Publisher
Springer Milan
Copyright
Copyright © 2017 by Springer-Verlag Italia
Subject
Mathematics; Mathematics, general; Applications of Mathematics; Theoretical, Mathematical and Computational Physics
ISSN
1578-7303
eISSN
1579-1505
D.O.I.
10.1007/s13398-017-0393-8
Publisher site
See Article on Publisher Site

Abstract

In this paper, we introduce the concepts of cyclic $$\varphi $$ φ -contractions in Menger PM-spaces and cyclic weak $$\phi $$ ϕ -contractions in generalized Menger PM-spaces. Based on these concepts, some fixed point results for cyclic $$\varphi $$ φ -contractions in Menger PM-spaces are obtained. Furthermore, some fixed point theorems for cyclic weak $$\phi $$ ϕ -contractions and cyclic $$\varphi $$ φ -contractions in generalized Menger PM-spaces are obtained by assuming that the number of cyclic sets is odd. An example is also given to show the validity of our main results.

Journal

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. MatemáticasSpringer Journals

Published: Mar 27, 2017

References

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