SOLUTION AND STABILITY OF TWO TYPES OF $n$-DIMENSIONAL QUARTIC FUNCTIONAL EQUATION IN GENERALIZED 2-NORMED SPACES

Murthy, S.; Govindhan, V.; Velan, M. Senthil

doi:10.12732/ijpam.v111i2.10

Cited by 7 publications

(7 citation statements)

References 10 publications

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“…In this paper, we have presented and discussed the results on Ulam stability in 2normed spaces provided in articles [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58]. In this way, we complement the paper [23], where the results from [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] have been surveyed. We have shown how to supplement or improve several of these results.…”

Section: Discussionmentioning

confidence: 99%

“…In this paper, we complement the content of [23], where the (less complicated) results from [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] have been surveyed. Here, we present and discuss the (more involved) outcomes on Ulam stability in 2-normed spaces provided in [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58].…”

Section: Introductionmentioning

confidence: 99%

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On Ulam Stability of Functional Equations in 2-Normed Spaces—A Survey II

El‐hady

Brzdęk

2022

Symmetry

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Ulam stability is motivated by the following issue: how much an approximate solution of an equation differs from the exact solutions to the equation. It is connected to some other areas of investigation, e.g., optimization, approximation theory and shadowing. In this paper, we present and discuss the published results on such stability for functional equations in the classes of function-taking values in 2-normed spaces. In particular, we point to several pitfalls they contain and provide possible simple improvements to some of them. Thus we show that the easily noticeable symmetry between them and the analogous results proven for normed spaces is, in fact, mainly apparent. Our article complements the earlier similar review published in Symmetry (13(11), 2200) because it concerns the outcomes that have not been discussed in this earlier publication.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Ulam Stability of Functional Equations in 2-Normed Spaces—A Survey II

El‐hady

Brzdęk

2022

Symmetry

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“…A very similar situation is in [63] (Theorems 4.1 and 5.1), where the stability of a functional equation of type (11) (called the n-dimensional quartic functional equation) has been studied in the 2-normed spaces.…”

Section: Conflicts Of Interestmentioning

confidence: 93%

On Ulam Stability of Functional Equations in 2-Normed Spaces—A Survey

et al. 2021

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The theory of Ulam stability was initiated by a problem raised in 1940 by S. Ulam and concerning approximate solutions to the equation of homomorphism in groups. It is somehow connected to various other areas of investigation such as, e.g., optimization and approximation theory. Its main issue is the error that we make when replacing functions satisfying the equation approximately with exact solutions of the equation. This article is a survey of the published so far results on Ulam stability for functional equations in 2-normed spaces. We present and discuss them, pointing to the various pitfalls they contain and showing possible simple generalizations. In this way, in particular, we demonstrate that the easily noticeable symmetry between them and the analogous results obtained for the classical metric or normed spaces is in fact only apparent.

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“…We also investigate the generalized Hyers-Ulam stability of this functional equation in Banach Space using direct method and fixed point method. Furthermore, we can refer [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45].…”

Section: Introductionmentioning

confidence: 99%