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27 results on '"Cădariu, Liviu"'

1. Fixed points and the stability of the linear functional equations in a single variable

Author

Cadariu, Liviu and Manolescu, Laura

Subjects
Mathematics - Functional Analysis, 39B62, 39B72, 39B82, 47H10
Abstract

We prove that an interesting result concerning generalized Hyers-Ulam-Rassias stability of a linear functional equation obtained in 2014 by S.M. Jung, D. Popa and M.T. Rassias in Journal of Global Optimization is a particular case of a fixed point theorem given by us in 2012. Moreover, we give a characterization of functions that can be approximated with a given error, by the solution of the previously mention linear equation., Comment: 12 pages

Published
2022

17. Fixed Points and Stability for Functional Equations in Probabilistic Metric and Random Normed Spaces

Author

Radu Viorel and Cădariu Liviu

Subjects
Applied mathematics. Quantitative methods, T57-57.97, Analysis, QA299.6-433
Abstract

Abstract We prove a general Ulam-Hyers stability theorem for a nonlinear equation in probabilistic metric spaces, which is then used to obtain stability properties for different kinds of functional equations (linear functional equations, generalized equation of the square root, spiral generalized gamma equations) in random normed spaces. As direct and natural consequences of our results, we obtain general stability properties for the corresponding functional equations in (deterministic) metric and normed spaces.

Published
2009

18. Fixed Point Methods for the Generalized Stability of Functional Equations in a Single Variable

Author

Radu Viorel and Cădariu Liviu

Subjects
Applied mathematics. Quantitative methods, T57-57.97, Analysis, QA299.6-433
Abstract

Abstract We discuss on the generalized Ulam-Hyers stability for functional equations in a single variable, including the nonlinear functional equations, the linear functional equations, and a generalization of functional equation for the square root spiral. The stability results have been obtained by a fixed point method. This method introduces a metrical context and shows that the stability is related to some fixed point of a suitable operator.

Published
2008

19. Survey on Recent Ulam Stability Results Concerning Derivations

Author

Brzdęk, Janusz, Cădariu, Liviu, Ciepliński, Krzysztof, Fošner, Ajda, and Leśniak, Zbigniew

Subjects
Article Subject
Abstract

This is a survey presenting the most significant results concerning approximate (generalized) derivations, motivated by the notions of Ulam and Hyers-Ulam stability. Moreover, the hyperstability and superstability issues connected with derivations are discussed. In the section before the last one we highlight some recent outcomes on stability of conditions defining (generalized) Lie derivations.

Published
2016
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20. Fixed Point Theory and the Ulam Stability

Author

Brzdęk, Janusz, Cădariu, Liviu, and Ciepliński, Krzysztof

Subjects
Article Subject
Abstract

The fixed point method has been applied for the first time, in proving the stability results for functional equations, by Baker (1991); he used a variant of Banach's fixed point theorem to obtain the stability of a functional equation in a single variable. However, most authors follow the approaches involving a theorem of Diaz and Margolis. The main aim of this survey is to present applications of different fixed point theorems to the theory of stability of functional equations, motivated by a problem raised by Ulam in 1940.

Published
2014
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26. On the stability of an affine functional equation.

Author

Găvruţa, Laura, Cădariu, Liviu, and Găvruţa, Paşc

Subjects
FUNCTIONAL equations, STABILITY theory, DIFFERENTIAL equations, MATHEMATICS, FUNCTIONAL analysis
Abstract

In this paper, we obtain the general solution and we prove the generalized Hyers-Ulam stability for an affine functional equation. [ABSTRACT FROM AUTHOR]

Published
2013

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