相关论文: Existence, uniqueness, and approximation for solut…

We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…

Let $G(k)=\int_0^1g(x)e^{kx}dx$, $g\in L^1(0,1)$. The main result of this paper is the following theorem. {\bf Theorem}. {\it If $\limsup_{k\to +\infty}|G(k)|<\infty$, then $g=0$. There exists $g\not\equiv 0$, $g\in L^1(0,1)$, such that…

This work is devoted to the study of the existence of at least one weak solution to nonlocal equations involving a general integro-differential operator of fractional type. As a special case, we derive an existence theorem for the…

In this paper we obtain degree of approximation of functions in Lp by operators associated with their Fourier series using integral modulus of continuity. These results generalize many know results and are proved under less stringent…

A wide range of numerical methods exists for computing polynomial approximations of solutions of ordinary differential equations based on Chebyshev series expansions or Chebyshev interpolation polynomials. We consider the application of…

The following theorem is the main result of this note. Theorem 1. Let $(E, \|\cdot\|_E) $ be a rearrangement invariant Banach function space on the interval $[0, 1]$. If $E$ is isometric to $\L_p [0, 1]$ for some $1\le p<\infty$, then $E$…

In this work we will consider integral equations defined on the whole real line and look for solutions which satisfy some certain kind of asymptotic behavior. To do that, we will define a suitable Banach space which, to the best of our…

Subsequent to our recent work on Fourier spectrum characterization of Hardy spaces $H^p(\mathbb{R})$ for the index range $1\leq p\leq \infty,$ in this paper we prove further results on rational Approximation, integral representation and…

This paper deals with the local existence and uniqueness results for the solution of fractional differential equations with Hilfer-Hadamrd fractional derivative. Using Picard's approximations and generalizing the restrictive conditions…

This paper is committed to establishing the assumptions essential for the existence and uniqueness results of a fractional functional integrodifferential equation (FFIDE) having a derivative of generalized Hilfer type. Using the Picard…

In this paper, we analyze metrical approximations of functions $F :\Lambda times X \rightarrow Y$ by trigonometric polynomials and $\rho$-periodic type functions, where $\emptyset \neq \Lambda \subseteq {\mathbb R}^{n},$ $X$ and $Y $are…

In this note, we show a classical result on the local existence and uniqueness of a solution to an initial value problem subject to a Lipschitz condition. We use only elementary tools from mathematical analysis, without involving any…

This survey paper contains a detailed self-contained introduction to Korovkin-type theorems and to some of their applications concerning the approximation of continuous functions as well as of L^p-functions, by means of positive linear…

We present an alternative proof for the existence of solutions of stochastic functional differential equations satisfying a global Lipschitz condition. The proof is based on an approximation scheme in which the continuous path dependence…

Using the fixed point alternative theorem we establish the orthogonal stability of quadratic functional equation of Pexider type $f(x+y)+g(x-y)=h(x)+k(y)$, where $f, g, h, k$ are mappings from a symmetric orthogonality space to a Banach…

It is shown how the linear method of the Yosida-approximation of the derivative applies to solve possibly nonlinear abstract functional differential equations in both, the finite and infinite delay case. A generalization of the integral…

Approximations to the integral $\int_a^b\int_c^d f(x,y)\,dy\,dx$ are obtained under the assumption that the partial derivatives of the integrand are in an $L^p$ space, for some $1\leq p\leq\infty$. We assume ${\lVert f_{xy}\rVert}_p$ is…

We study integrability conditions for existence and nonexistence of a local-in-time integral solution of fractional semilinear heat equations with rather general growing nonlinearities in uniformly local $L^p$ spaces. Our main results about…

We obtain new equitightness and $C([0,T];L^p(\mathbb{R}^N))$-convergence results for finite-difference approximations of generalized porous medium equations of the form $$ \partial_tu-\mathfrak{L}[\varphi(u)]=g\qquad\text{in…

Let $\sigma>0$. For $1\le p\le \infty$, the Bernstein space $B^p_{\sigma}$ is a Banach space of all $f\in L^p(R)$ such that $f$ is bandlimited to $\sigma$; that is, the distributional Fourier transform of $f$ is supported in $[-\sigma,…