# 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

, Volume 112 (2) – Mar 27, 2017
14 pages

/lp/springer_journal/fixed-point-results-for-cyclic-contractions-in-menger-pm-spaces-and-8OdijmH0aL
Publisher
Springer Milan
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

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