Generalized Hyers-Ulam Stability of Trigonometric Functional Equations

Elqorachi, Elhoucien; Rassias, Michael Th.

doi:10.3390/math6050083

Cited by 10 publications

(4 citation statements)

References 52 publications

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“…Note that (3) is a particular case of (7). For comments on some other particular cases of this equation, see [10,24,[31][32][33][34][35].…”

Section: Definitionmentioning

confidence: 99%

See 1 more Smart Citation

On Ulam Stability with Respect to 2-Norm

Brzdęk

2023

Symmetry

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The Ulam stability of various equations (e.g., differential, difference, integral, and functional) concerns the following issue: how much does an approximate solution of an equation differ from its exact solutions? This paper presents methods that allow to easily obtain numerous general Ulam stability results with respect to the 2-norms. In four examples, we show how to deduce them from the already known outcomes obtained for classical normed spaces. We also provide some simple consequences of our results. Thus, we demonstrate that there is a significant symmetry between such results in classical normed spaces and in 2-normed spaces.

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“…Note that (3) is a particular case of (7). For comments on some other particular cases of this equation, see [10,24,[31][32][33][34][35].…”

Section: Definitionmentioning

confidence: 99%

“…An ample discussion on various possible definitions of such stability is provided in [4]. Numerous examples of recent Ulam stability results as well as further related information and references are also given in [5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

On Ulam Stability with Respect to 2-Norm

Brzdęk

2023

Symmetry

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“…It is a type of stability which was initiated by a mathematical question by Ulam [24] and subsequent partial answers by Hyers [9] and Rassias [16]. The investigation of such stability has been performed in various contexts of mathematics like functional equations [5,6], isometries [12,17], etc.…”

Section: Introductionmentioning

confidence: 99%

Existence, error estimation, rate of convergence, Ulam-Hyers stability, well-posedness and limit shadowing property related to a fixed point problem

Choudhury

Metiya

Kundu³

2022

bspm

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In this paper we consider a fixed point problem where the mapping is supposed to satisfy a generalized contractive inequality involving rational terms. We first prove the existence of a fixed point of such mappings. Then we show that the fixed point is unique under some additional assumptions. We investigate four aspects of the problem, namely, error estimation and rate of convergence of the fixed point iteration, Ulam-Hyers stability, well-psoedness and limit shadowing property. In the existence theorem we use an admissibility condition. Two illustration are given. The research is in the line with developing fixed point approaches relevant to applied mathematics.

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“…Problems of that type are very natural for difference, differential, functional and integral equations and many examples of recent results concerning their stability as well as further references can be found in [6,7].…”

Section: Introductionmentioning

confidence: 99%