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.
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas – Springer Journals
Published: Mar 27, 2017
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