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On Hyperstability of the Two-Variable Jensen Functional Equation on Restricted Domain

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Mathematical Analysis and Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 154))

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Abstract

We present a method that allows to study approximate solutions to the two-variable Jensen functional equation

$$\displaystyle 2f\Big (\frac {x+z}{2},\frac {y+w}{2}\Big )=f(x,y)+f(z,w) $$

on a restricted domain. Namely, we show that (under some weak natural assumptions) functions that satisfy the equation approximately (in some sense) must be actually solutions to it. The method is based on a quite recent fixed point theorem in some functions spaces and can be applied to various similar equations in many variables. Our outcomes are connected with the well-known issues of Ulam stability and hyperstability.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences and Techniques, Sidi Mohamed ben abdellah University, Fez, Morocco

    Iz-iddine EL-Fassi

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  1. Iz-iddine EL-Fassi
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Editors and Affiliations

  1. Department of Mathematics, Zografou Campus, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

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EL-Fassi, Ii. (2019). On Hyperstability of the Two-Variable Jensen Functional Equation on Restricted Domain. In: Rassias, T., Pardalos, P. (eds) Mathematical Analysis and Applications. Springer Optimization and Its Applications, vol 154. Springer, Cham. https://doi.org/10.1007/978-3-030-31339-5_5

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