Dorian Popa
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View article: Steklov Type Operators and Functional Equations
Steklov Type Operators and Functional Equations Open
We consider sequences of Steklov type operators and an associated functional equation. For a suitable sequence, we establish asymptotic formulas.
View article: Best Constant in Ulam Stability for the Third Order Linear Differential Operator with Constant Coefficients
Best Constant in Ulam Stability for the Third Order Linear Differential Operator with Constant Coefficients Open
The authors of the present paper previously proved the Ulam stability for the n-th-order linear differential operator with constant coefficients. They obtained its best Ulam constant for the case of distinct roots of the characteristic equ…
View article: On Ulam Stability of a Partial Differential Operator in Banach Spaces
On Ulam Stability of a Partial Differential Operator in Banach Spaces Open
In this paper, we prove that, if infx∈A|f(x)|=m>0, then the partial differential operator D defined by D(u)=∑k=1nfk∂u∂xk−fu, where f,fi∈C(A,R),u∈C1(A,X),i=1,…,n,I⊂R is an interval, A=I×Rn−1 and X is a Banach space, is Ulam stable with the …
View article: On Ulam stability of a second order linear difference equation
On Ulam stability of a second order linear difference equation Open
In this paper we obtain some Ulam stability results for the second order and the third order linear difference equation with nonconstant coefficients in a Banach space. The main idea of the approach is to decompose the second order linear …
View article: The Best Ulam Constant of the Fréchet Functional Equation
The Best Ulam Constant of the Fréchet Functional Equation Open
In this paper, we prove the Ulam stability of the Fréchet functional equation f(x+y+z)+f(x)+f(y)+f(z)=f(x+y)+f(y+z)+f(z+x) arising from the characterization of inner product spaces and we determine its best Ulam constant. Using this result…
View article: On the Best Ulam Constant of the Linear Differential Operator with Constant Coefficients
On the Best Ulam Constant of the Linear Differential Operator with Constant Coefficients Open
The linear differential operator with constant coefficients D(y)=y(n)+a1y(n−1)+…+any,y∈Cn(R,X) acting in a Banach space X is Ulam stable if and only if its characteristic equation has no roots on the imaginary axis. We prove that if the ch…
View article: On the best Ulam constant of the linear differential operator with constant coefficients
On the best Ulam constant of the linear differential operator with constant coefficients Open
The linear differential operator with constant coefficients $$D(y)=y^{(n)}+a_1 y^{(n-1)}+\ldots+a_n y,\quad y\in \mathcal{C}^{n}(\mathbb{R}, X)$$ acting in a Banach space $X$ is Ulam stable if and only if its characteristic equation has no…
View article: Ulam Stability of a Second Linear Differential Operator with Nonconstant Coefficients
Ulam Stability of a Second Linear Differential Operator with Nonconstant Coefficients Open
In this paper, we obtain a result on Ulam stability for a second order differential operator acting on a Banach space. The result is connected to the existence of a global solution for a Riccati differential equation and some appropriate c…
View article: On Approximate Aesthetic Curves
On Approximate Aesthetic Curves Open
Symmetry plays an essential role for generating aesthetic forms. The curve is the basic element used by designers to obtain aesthetic forms. A curve with a linear logarithmic curvature graph gradient is called aesthetic curve. The aestheti…
View article: Bounds for solutions of linear differential equations and Ulam stability
Bounds for solutions of linear differential equations and Ulam stability Open
We obtain Gronwall type bounds for the solutions of a linear system of differential equations.As applications we get results on Ulam stability for linear differential equations and linear systems of differential equations.
View article: <i>Report of Meeting</i> 18th International Conference on Functional Equations and Inequalities, Będlewo, Poland, June 9–15, 2019
<i>Report of Meeting</i> 18th International Conference on Functional Equations and Inequalities, Będlewo, Poland, June 9–15, 2019 Open
1), Finland (1), France (1), Germany (2), Hungary (6), India (1), Israel (1), Morocco (1), Poland (30), Romania (5), Serbia (1), South Africa (1), USA (1).The conference was opened on Monday, June 10, by Professors Janusz Brzdęk, the Chair…
View article: Best Ulam constant for a linear difference equation
Best Ulam constant for a linear difference equation Open
In this paper we provide some results on Ulam stability for the linear difference equation of order one in Banach spaces and we determine its best Ulam constant. The main result is applied to a process of loan amortization.
View article: On Ulam stability of the second order linear differential equation
On Ulam stability of the second order linear differential equation Open
We obtain a result on Ulam stability for a linear differential equation in Banach spaces. As application we give a result on the stability of Heun’s differential equation.
View article: Hyers-Ulam stability of the Laplace operator
Hyers-Ulam stability of the Laplace operator Open
We investigate the Hyers-Ulam stability of the Laplace operator ∆ and of a multiple of it, acting on suitable domains.Moreover, we obtain an explicit representation of the Hyers-Ulam constant.
View article: Steklov averages as positive linear operators
Steklov averages as positive linear operators Open
We introduce a class of positive linear operators defined by Steklov means, investigate their properties and prove that the Weierstrass operators can be approximated in terms of the Steklov averages.