Some remarks on the stability of the multi-Jensen equation

Schwaiger, Jens

doi:10.2478/s11533-013-0215-y

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Cited by 2 publications

(2 citation statements)

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“…Our results are significant supplements and/or generalizations of some results from [1,12,13,14,16,18,23,27,29,30,31].…”

Section: Resultssupporting

confidence: 81%

On an equation characterizing multi-Jensen-quadratic mappings and its Hyers–Ulam stability via a fixed point method

Bahyrycz

Ciepliński

2016

J. Fixed Point Theory Appl.

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“…Our results are significant supplements and/or generalizations of some results from [1,12,13,14,16,18,23,27,29,30,31].…”

Section: Resultssupporting

confidence: 81%

On an equation characterizing multi-Jensen-quadratic mappings and its Hyers–Ulam stability via a fixed point method

Bahyrycz

Ciepliński

2016

J. Fixed Point Theory Appl.

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“…This result is a tool for obtaining a generalized Hyers-Ulam stability or hyperstability of this equation for particular control functions, which is presented in several examples. Our results are significant counterparts of some classical outcomes from [1,11,22,23,35] and recent results from [2][3][4]10,[17][18][19][20][24][25][26][27]31,32,34,36].…”

Section: Introductionsupporting

confidence: 79%

On Stability and Hyperstability of an Equation Characterizing Multi-Cauchy–Jensen Mappings

Bahyrycz

Olko

2018

Results Math

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Recently, functions of several variables satisfying, with respect to each variable, some functional equation (among them Cauchy's, Jensen's, quadratic and other ones) have been studied. We give a new characterization of multi-Cauchy-Jensen mappings, which states that a function fulfilling some equation on a restricted domain is multi-Cauchy-Jensen. Next, using a fixed point theorem, it is proved that a function which approximately satisfies (on restricted domain) the equation characterizing such functions is close (in some sense) to the solution of the equation. This result is a tool for obtaining a generalized Hyers-Ulam stability or hyperstability of this equation for particular control functions, which is presented in several examples.Mathematics Subject Classification. 39B52, 39B82, 39B72, 47H10.

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Some remarks on the stability of the multi-Jensen equation

Abstract: MSC:39B52

Cited by 2 publications

References 7 publications

On an equation characterizing multi-Jensen-quadratic mappings and its Hyers–Ulam stability via a fixed point method

On an equation characterizing multi-Jensen-quadratic mappings and its Hyers–Ulam stability via a fixed point method

On Stability and Hyperstability of an Equation Characterizing Multi-Cauchy–Jensen Mappings

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