Common Fixed Points for Nonlinear Quasi-Contractions of Ćirić Type

Abstract

We establish common fixed points theorems for two self-mappings satisfying a nonlinear contractive condition of Ćirić type with aQ-function. Furthermore, using the scalarization method, we deduce some results of common fixed point in tvs-cone metric spaces with ac-distance. As application, we give a positive answer to the question of Ćirić et al. posed in 2012. Our results extend and generalize many recent results.

Fundamental Questions and New Counterexamples for b-Metric Spaces and Fatou Property

“…Clearly,Ćirić fixed point theorem is an actually generalization of the Banach contraction principle [15], Kannan's fixed point theorem [16] and Chatterjea's fixed point theorem [17]. Due to the importance and application potential to quantitative sciences, the generalizations ofĆirić fixed point theorem have been investigated heavily by many authors in various distinct directions over the past 20 years; see, e.g., [4,5,8,12,[18][19][20][21] and the related references therein. Recently, Amini-Harandi [4] proved a generalization ofĆirić fixed point theorem in the setting of b-metric spaces with Fatou property.…”