On an equation characterizing multi-cauchy-jensen mappings and its Hyers-Ulam stability

Bahyrycz, Anna; Ciepliński, Krzysztof; Olko, Jolanta

doi:10.1016/s0252-9602(15)30059-x

Cited by 17 publications

(15 citation statements)

References 25 publications

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“…(3) on restricted domain. This result generalizes Theorem 3.2 from [9]. The proof is based on a fixed point result that can be derived from [14] (Theorem 1).…”

Section: Stability Of Multi-cauchy-jensen Mappings On Restricted Domainsupporting

confidence: 54%

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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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“…(3) on restricted domain. This result generalizes Theorem 3.2 from [9]. The proof is based on a fixed point result that can be derived from [14] (Theorem 1).…”

Section: Stability Of Multi-cauchy-jensen Mappings On Restricted Domainsupporting

confidence: 54%

“…In [9], a characterization of multi-Cauchy-Jensen mappings was proved. Using our notations we can rephrase it in the following form.…”

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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“…(their solutions are said to be additive and Jensen mappings, respectively) are particular cases of (1). For more information about equations (2) and (3) and some applications of them ((3) is called the Jensen equation and it is connected with the notion of convexity) we refer the reader for example to [14,15].…”

Section: Background and Motivationmentioning

confidence: 99%

On Ulam Stability of a Functional Equation

Ciepliński

2020

Results Math

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“…In this section, we show the generalized Hyers-Ulam stability of equation (2.1) in complete non-Archimedean normed spaces (its stability in Banach spaces was proved in [2]). The proof is based on a fixed point result that can be derived from [7,Theorem 1].…”

Section: Stability Of An Equation Characterizing Multi-cauchy-jensen mentioning

confidence: 99%

On Hyers–Ulam stability of two functional equations in non-Archimedean spaces

Bahyrycz

Ciepliński

Olko

2016

J. Fixed Point Theory Appl.

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On an equation characterizing multi-cauchy-jensen mappings and its Hyers-Ulam stability

Cited by 17 publications

References 25 publications

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

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

On Ulam Stability of a Functional Equation

On Hyers–Ulam stability of two functional equations in non-Archimedean spaces

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