Parameterized curve as attractors of some countable iterated function systems

summary:In this paper we will demonstrate that, in some conditions, the attractor of a countable iterated function system is a parameterized curve. This fact results by generalizing a construction of J. E. Hutchinson [Hut81]

Parameterized curve as attractors of some countable iterated function systems

summary:In this paper we will demonstrate that, in some conditions, the attractor of a countable iterated function system is a parameterized curve. This fact results by generalizing a construction of J. E. Hutchinson [Hut81]

A New Kind of Nonlinear Quasicontractions in Metric Spaces

Starting from two extensions of the Banach contraction principle due to Ćirić (1974) and Wardowski (2012), in the present paper we introduce the concepts of Ćirić type ψ F -contraction and ψ F -quasicontraction on a metric space and give some sufficient conditions under which the respective mappings are Picard operators. Some known fixed point results from the literature can be obtained as particular cases.</jats:p

Continuous dependence on a parameter of the countable fractal interpolation function

In this paper we will show that, if a countable interpolation data depends continuously on a parameter and some proper continuity conditions are fulfilled, then its associated attractor and the corresponding countable fractal interpolation function depends also continuously on the respective parameter. An example in R^2 is given.</jats:p

A New Kind of Nonlinear Quasicontractions in Metric Spaces

Starting from two extensions of the Banach contraction principle due to Ćirić (1974) and Wardowski (2012), in the present paper we introduce the concepts of Ćirić type &psi; F -contraction and &psi; F -quasicontraction on a metric space and give some sufficient conditions under which the respective mappings are Picard operators. Some known fixed point results from the literature can be obtained as particular cases

Generalized F-Contractions on Product of Metric Spaces

Our purpose in this paper is to extend the fixed point results of a ψ F -contraction introduced by Secelean N.A. and Wardowski D. ( ψ F -Contractions: Not Necessarily Nonexpansive Picard Operators, Results. Math.70(3), 415–431 (2016)) defined on a metric space X into itself to the case of mapping defined on the product space X I , where I is a set of positive integers (natural numbers). Some improvements to the conditions imposed on function F and space X are provided. An illustrative example is given.</jats:p

Expansive mappings on bounded sets and their application to rational integral equations

AbstractThe aim of this paper is to introduce a new condition of expansiveness which extends the class of the known expansive-type mappings in the domain of closed and bounded subsets of a metric space. For the sum of an expansive mapping in a proposed sense defined on a closed convex and bounded subset of a Banach space and a continuous and compact operator, there are proved some fixed point theorems. There are also provided some examples which motivate our research. Moreover, an application to the existence problem of periodic solutions of nonlinear integral equations with a rational part is provided.</jats:p

Suzuki ψF-contractions and some fixed point results

The purpose of this paper is to combine and extend some recent fixed point results of Suzuki, T., [A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313–5317] and Secelean, N. A. &amp; Wardowski, D., [ψF-contractions: not necessarily nonexpansive Picard operators, Results Math., 70 (2016), 415–431]. The continuity and the completeness conditions are replaced by orbitally continuity and orbitally completeness respectively. It is given an illustrative example of a Picard operator on a non complete metric space which is neither nonexpansive nor expansive and has a unique continuity point.</jats:p