Fixed points for cyclic φ-contractions in generalized metric spaces

Abstract

In this paper, we obtain a fixed point theorem for mappings satisfying cyclic ϕ-contractive conditions in complete metric spaces, which gives a positive answer to the question raised by Radenović (Fixed Point Theory Appl. 2015:189, 2015). We also find that this result and the fixed point result satisfying cyclic weak φ-contractions given by Karapınar (Appl. Math. Lett. 24:822-825, 2011) are independent of each other. Furthermore, when the number of cyclic sets is odd, we obtain fixed point theorems satisfying cyclic weak φ-contractions and cyclic ϕ-contractions in the setting of generalized metric spaces.

Generalized cyclic contractions and coincidence points involving a control function on partial metric spaces

“…After that, several generalized control functions were used to obtain fixed-point results in various spaces. The results of [19][20][21][22] have become the source of motivation of this study. In this work, we introduce the concept of cyclic representation of a nonempty set with respect to a pair of mappings and use it to prove a coincidence point and common fixed-point result for a pair of self-mappings satisfying some generalized contraction-type conditions involving a control function in partial metric spaces.…”