Results 1 to 10 of about 3,315 (113)
The Cauchy Exponential of Linear Functionals on the Linear Space of Polynomials
Mathematics, 2023 In this paper, we introduce the notion of the Cauchy exponential of a linear functional on the linear space of polynomials in one variable with real or complex coefficients using a functional equation by using the so-called moment equation. It seems that
Francisco Marcellán, Ridha Sfaxi
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Variants of the functional equation of Cauchy
Lietuvos Matematikos Rinkinys, 2004 In this paper solution of the Cauchy functional equation and variants of it are considered.
Juozas Mačys
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Some hyperstability and stability results for the Cauchy and Jensen equations
Journal of Inequalities and Applications, 2022 In this paper we give some hyperstability and stability results for the Cauchy and Jensen functional equations on restricted domains. We provide a simple and short proof for Brzdȩk’s result concerning a hyperstability result for the Cauchy equation.
Mohammad Bagher Moghimi, Abbas Najati
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Alienation of Drygas’ and Cauchy’s Functional Equations
Annales Mathematicae Silesianae, 2021 Inspired by the papers [2, 10] we will study, on 2-divisible groups that need not be abelian, the alienation problem between Drygas’ and the exponential Cauchy functional equations, which is expressed by the equation f(x+y)+g(x+y)g(x-y)=f(x)f(y)+2g(x)+g ...
Aissi Youssef +2 more
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On a General Conditional Cauchy Functional Equation [PDF]
Sahand Communications in Mathematical AnalysisLet $(G,+)$ be an abelian group and $Y$ a linear space over the field $\Bbb{F}\in\{\Bbb{R}, \Bbb{C}\}$. In this paper, we investigate the conditional Cauchy functional equation \[f(x+y)\neq af(x)+bf(y)\quad\Rightarrow \quad f(x+y)=f(x)+f(y),\quad x,y\in
Elham Mohammadi +2 more
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A Fixed Point Approach to the Stability of a Cauchy-Jensen Functional Equation
Abstract and Applied Analysis, 2012 We find out the general solution of a generalized Cauchy-Jensen functional equation and prove its stability. In fact, we investigate the existence of a Cauchy-Jensen mapping related to the generalized Cauchy-Jensen functional equation and prove its ...
Jae-Hyeong Bae, Won-Gil Park
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Intuitionistic fuzzy almost Cauchy–Jensen mappings
Demonstratio Mathematica, 2016 In this paper, we first investigate the Hyers–Ulam stability of the generalized Cauchy–Jensen functional equation of p-variable f(∑i=1paixi)=∑i=1paif(xi)$f\left(\sum\nolimits_{i = 1}^p {a_i x_i } \right) = \sum\nolimits_{i = 1}^p {a_i f(x_i )}$ in an ...
Gordji M. E., Abbaszadeh S.
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Mathematics, 2023 Cauchy problems are considered for families of, generally speaking, non-Volterra functional differential equations of the second order. For each family considered, in terms of the parameters of this family, necessary and sufficient conditions for the ...
Eugene Bravyi
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Electronic Journal of Qualitative Theory of Differential Equations, 2013 Conditions for the unique solvability of the Cauchy problem for a family of scalar functional differential equations are obtained. These conditions are sufficient for the solvability of the Cauchy problem for every equation from the family and are ...
Eugene Bravyi
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Local stability of mappings on multi-normed spaces
Advances in Difference Equations, 2020 First we investigate the Hyers–Ulam stability of the Cauchy functional equation for mappings from bounded (unbounded) intervals into Banach spaces. Then we study the Hyers–Ulam stability of the functional equation f ( x y ) = x g ( y ) + h ( x ) y $f(xy)=
Choonkil Park +4 more
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