Displaying similar documents to “Connections between some measures of non-compactness and associated operators.”

Contractions on probabilistic metric spaces: examples and counterexamples.

Berthold Schweizer, Howard Sherwood, Robert M. Tardiff (1988)

Stochastica

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The notion of a contraction mapping for a probabilistic metric space recently introduced by T. L. Hicks is compared with the notion previously introduced by V. L. Sehgal and A. T. Bharucha-Reid. By means of appropriate examples, it is shown that these two notions are independent. It is further shown that every Hick's contraction on a PM space (S,F,t) is an ordinary metric contraction with respect to a naturally defined metric on that space; and it is again pointed out that, in Menger...

Some properties of the Hausdorff distance in metric spaces.

Jozef Banas, Antonio Martinón (1990)

Extracta Mathematicae

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Some properties of the Hausdorff distance in complete metric spaces are discussed. Results obtained in this paper explain ideas used in the theory of measures of noncompactness.

Fractals of generalized F− Hutchinson operator

Talat Nazir, Sergei Silvestrov, Mujahid Abbas (2016)

Waves, Wavelets and Fractals

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The aim of this paper is to construct a fractal with the help of a finite family of F− contraction mappings, a class of mappings more general than contraction mappings, defined on a complete metric space. Consequently, we obtain a variety of results for iterated function systems satisfying a different set of contractive conditions. Some examples are presented to support the results proved herein. Our results unify, generalize and extend various results in the existing literature. ...