相关论文: Existence, uniqueness, and approximation for solut…
The objective of this paper is to construct separable Banach spaces $S{D^p}[\mathbb{R}^\infty]$ for $1\leq p \leq \infty$, each of which contains the $L^p[\mathbb{R}^\infty] $ spaces, as well as finitely additive measures, as compact dense…
Picard's iteration has been used to prove the existence and uniqueness of the solution for stochastic integral equations, here we use Schauder's fixed point theorem to give a new existence theorem about the solution of a stochastic integral…
We establish square function estimates for integral operators on uniformly rectifiable sets by proving a local $T(b)$ theorem and applying it to show that such estimates are stable under the so-called big pieces functor. More generally, we…
We prove existence and uniqueness of L^p solutions of reflected backward stochastic differential equations with p-integrable data and generators satisfying the monotonicity condition. We also show that the solution may be approximated by…
We consider several problems at or beyond endpoint in harmonic analysis. The solutions of these problems are related to the estimates of some classes of sublinear operators. To do this, we introduce some new functions spaces…
In this paper we give an explicit description of the universal unitary completion of certain locally Q_p-analytic representations of GL_2(F), where F is a finite extension of Q_p (this generalizes some results of Berger-Breuil for F=Q_p).…
This paper is devoted to the study of $L_p$ Lyapunov-type inequalities for linear systems of equations with Neumann boundary conditions and for any constant $p \geq 1$. We consider ordinary and elliptic problems. The results obtained in the…
In this work, we prove the generalised Hyer Ulam stability of the following functional equation \begin{equation}\label{Eq-1} \phi(x)+\phi(y)+\phi(z)=q \phi\left(\sqrt[s]{\frac{x^s+y^s+z^s}{q}}\right),\qquad |q| \leq 1 \end{equation} and $s$…
The discrete functional $L_p$ Minkowski problem is posed and solved. As a consequence, the general affine P\'{o}lya-Szeg\"{o} principle and the general affine Sobolev inequalities are established.
The existence of positive, pointwise decaying at infinity, weak solutions to a fractional $p$-Laplacian problem in the whole space and with singular reaction is established. Truncation arguments, variational methods, as well as suitable a…
The existence of solutions to Cauchy type problems of linear Riemann-Liouville fractional differential equations with variable coefficients is considered in a space of integrable functions. First, we consider the existence and uniqueness of…
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional equation), quantum field theory (Schwinger-Dyson equations)…
For each $1\leq p<\infty$ a space of integrable Schwartz distributions, $L^'^{\,p}$, is defined by taking the distributional derivative of all functions in $L^p$. Here, $L^p$ is with respect to Lebesgue measure on the real line. If $f\in…
Hyre-Ulam stability of functional equation in single variable is studied in non-triangular metric spaces. We derive it as applications of some fixed point results developed on the said structure. A general version of Baker's theorem is also…
The fundamental Filippov-Wazwski Relaxation Theorem states that the solution set of an initial value problem for a locally Lipschitz inclusion is dense in the solution set of the same initial value problem for the corresponding relaxation…
In this paper we consider the recurrent equation $$\Lambda_{p+1}=\frac1p\sum_{q=1}^pf\bigg(\frac{q}{p+1}\bigg)\Lambda_{q}\Lambda_{p+1-q}$$ for $p\ge 1$ with $f\in C[0,1]$ and $\Lambda_1=y>0$ given. We give conditions on $f$ that guarantee…
In this paper, the notion of $\mathbb{C}$-simulation function is introduced and the existence and uniqueness of common fixed points of two self-mappings satisfying contractive conditions in the setting of complex valued metric spaces via…
We propose a fast and stable method for constructing matrix approximations to fractional integral operators applied to series in the Chebyshev fractional polynomials. This method utilizes a recurrence relation satisfied by the fractional…
We study the solvability of a quadratic integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions defined, bounded and continuous on an unbounded…
We prove matching direct and inverse theorems for (algebraic) polynomial approximation with doubling weights $w$ having finitely many zeros and singularities (i.e., points where $w$ becomes infinite) on an interval and not too ``rapidly…