We note that Theorem 2.3 [1] is a consequence of the same theorem for one map.

Let X denote a locally compact metric space and φ : X → X be a continuous map. In the 1970s L. Zadeh presented an extension principle, helping us to fuzzify the dynamical system (X, φ), i.e., to obtain a map Φ for the space of fuzzy sets on X. We extend an idea mentioned in [P. Diamond, A. Pokrovskii, Chaos, entropy and a generalized extension principle, Fuzzy Sets and Systems 61 (1994)] and we...

This paper is devoted to prove the S. L. Singh’s common fixed point Theorem for commuting mappings in cone metric spaces. In this framework, we introduce the notions of generalized Kannan contraction, generalized Zamfirescu contraction and generalized Weak contraction for a pair of mappings, proving afterward fixed point results.

The main purpose of this paper is to study the approximate best proximity pair of cyclic maps and their diameter in fuzzy normed spaces defined by Bag and Samanta. First, approximate best point proximity points on fuzzy normed linear spaces are defined and four general lemmas are given regarding approximate fixed point and approximate best proximity pair of cyclic maps on fuzzy normed spaces. U...

Cyclic weak φ-contraction mapping is introduced in Menger space and fixed point theorem for such mappings are studied in Menger space. Mathematics Subject Classification 47H10, 54H25

* Correspondence: ming@mail. nhcue.edu.tw Department of Applied Mathematics, National Hsinchu University of Education, Hsin-Chu, Taiwan Full list of author information is available at the end of the article Abstract In this article, we introduce the notions of (j φ)-weak contraction mappings and (ψ φ)-weak contraction mappings in complete generalized metric spaces and prove two theorems which a...

We consider holomorphic self-maps φ of the unit ball B in C (N = 1, 2, 3, ...). In the one-dimensional case, when φ has no fixed points in D := B and is of hyperbolic type, there is a classical renormalization procedure due to Valiron which allows to semi-linearize the map φ, and therefore, in this case, the dynamical properties of φ are well understood. In what follows, we generalize the class...

Given a discrete-time random dynamical system represented by cocycle of non-singular measurable maps, we may obtain information on quantities studying the Perron–Frobenius operators associated to maps. Of particular interest is second-largest Lyapunov exponent for operators, λ2, which can tell us about mixing rates and decay correlations in system. We prove generalized theorem cocycles bounded ...