Approximation of an Additive <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:msub><mml:mrow><mml:mi>ϱ</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>ϱ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:math>-Random Operator Inequality

Jang, Sun Young; Saadati, Reza

doi:10.1155/2020/7540303

Cited by 5 publications

(3 citation statements)

References 21 publications

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“…A complete C * AVFN-space is called a C * -algebra valued fuzzy Banach space (in short, a C * AVFB-space). Recently, some authors discussed the approximation of functional equations in several spaces by using a direct technique and a fixed point technique; for fuzzy Menger normed algebras, see [24]; for fuzzy metric spaces, see [25,26]; for FN spaces, see [27]; for non-Archimedean random Lie C * -algebras, see [28]; for non-Archimedean random normed spaces, see [29]; for random multi-normed space, see [30]; and we also refer the reader to [31][32][33][34].…”

Section: Definitionmentioning

confidence: 99%

$C^{*}$-Algebra valued fuzzy normed spaces with application of Hyers–Ulam stability of a random integral equation

et al. 2020

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In this paper, we consider $C^{*}$ C ∗ -algebra valued fuzzy normed spaces. We study the random integral equation $(\frac{1}{2c})\int _{x-cd}^{x+cd}u(\gamma ,\tau ,d_{0})\,d\tau =u( \gamma ,x,d)$ ( 1 2 c ) ∫ x − c d x + c d u ( γ , τ , d 0 ) d τ = u ( γ , x , d ) which is related to the stochastic wave equation. In addition, using a $C^{*}$ C ∗ -algebra valued fuzzy controller function, we consider its $C^{*}$ C ∗ -algebra valued fuzzy Hyers–Ulam stability.

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Section: Definitionmentioning

confidence: 99%

$C^{*}$-Algebra valued fuzzy normed spaces with application of Hyers–Ulam stability of a random integral equation

et al. 2020

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“…For a number of years now, many interesting results of the stability problems to several functional equations (or involving the range from additive functional equation to sextic functional equation) have been investigated; see, e.g., [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Nearly General Septic Functional Equation

Chang

Lee

Roh

2021

Journal of Function Spaces

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If a mapping can be expressed by sum of a septic mapping, a sextic mapping, a quintic mapping, a quartic mapping, a cubic mapping, a quadratic mapping, an additive mapping, and a constant mapping, we say that it is a general septic mapping. A functional equation is said to be a general septic functional equation provided that each solution of that equation is a general septic mapping. In fact, there are a lot of ways to show the stability of functional equations, but by using the method of G a ˘ vruta, we examine the stability of general septic functional equation ∑ i = 0 8 C 8 i − 1 8 − i f x + i − 4 y = 0 which considered. The method of G a ˘ vruta as just mentioned was given in the reference Gavruta (1994).

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“…In this paper, we study distribution functions with the ranges in a class of matrix algebras [1][2][3] and introduce the concept of a matrix Menger normed algebra using the generalized triangular norm which is a generalization of an MB-algebra [4], i.e., a Menger normed space with algebraic structures [5][6][7][8]. This concept helps us to study intuitionistic spaces and their generalization, i.e., neutrosophic spaces introduced by Smarandache [9,10].…”

Section: Introductionmentioning

confidence: 99%