Stability of a Cauchy-Jensen Functional Equation in Quasi-Banach Spaces

Bae, Jae-Hyeong; Park, Won-Gil

doi:10.1155/2010/151547

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Cited by 5 publications

(2 citation statements)

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“…Jun, Jung, and Lee [9] obtained the stability on a bi-Jensen functional equation in Banach spaces. Additionally, the authors [10] proved the stability on a Cauchy-Jensen functional equation Banach spaces.…”

Section: Introductionmentioning

confidence: 98%

Stability of Bi-Additive Mappings and Bi-Jensen Mappings

Bae

Park

2021

Symmetry

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Section: Introductionmentioning

confidence: 98%

Stability of Bi-Additive Mappings and Bi-Jensen Mappings

Bae

Park

2021

Symmetry

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“…To finish this introductory section let us finally mention that some results on the stability of Cauchy-Jensen mappings can be found in [6,7,[24][25][26][27]31,32].…”

Section: Introductionmentioning

confidence: 99%

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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