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Survey on Recent Ulam Stability Results Concerning Derivations

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...

Survey on Recent Ulam Stability Results Concerning Derivations

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...

Ulam’s Type Stability and Fixed Points Methods 2016

concerning approximate derivations (also generalized and/or Lie) as well as the hyperstability and superstability issues connected with them. Janusz Brzdęk Liviu Cădariu Krzysztof Ciepliński Ajda Fošner

Fixed Point Theory and the Ulam Stability

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...

Fixed Point Theory and the Ulam Stability

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...

Fixed Point Theory and the Ulam Stability

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...

Ulam’s Type Stability and Fixed Points Methods

LiviuCădariu Krzysztof Ciepliński Ajda Fošner Zbigniew Leśniak Bing Xu

Ulam’s Type Stability and Fixed Points Methods

LiviuCădariu Krzysztof Ciepliński Ajda Fošner Zbigniew Leśniak Bing Xu

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

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...

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

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...