Related papers: A L'hospital's rule for multivariable functions
For students and their lecturers and instructors interested in the natural problem of a possible generalization of l'Hopital's rule for functions depending on two or more variables, we offer our approach. For instructors, we discuss the…
The aim is to formulate a discrete analog of L'Hospital's rule and describe some of its applications. While the usual L'Hospital's rule is very well known, its discrete analog apparently was not in the literature. Since the L'Hospital's…
We introduce a generalization of Cauchy's mean value theorem for regulated functions. Building on this, we extend both L'Hospital's rule and L'Hospital's monotone rule to quotients of regulated functions. We demonstrate that our extended…
In calculus, l'Hopital's rule provides a simple way to evaluate the limits of quotient functions when both the numerator and denominator vanish. But what happens when we move beyond real functions on a real interval? In this article, we…
The aim of the present article is to establish the connection between the existence of the limit along the normal and an admissible limit at a fixed boundary point for holomorphic functions of several complex variables.
We look for pointwise bounds on a plurisubharmonic function near its singularity point, given the value of its generalized Lelong number with respect to a plurisubharmonic weight. To this end, an extremal problem is considered. In certain…
Let $-\infty \leq a<b\leq \infty $. Let $f$ and $g$ be differentiable functions on $(a,b)$ and let $g^{\prime }\neq 0$ on $(a,b)$. By introducing an auxiliary function $H_{f,g}:=\left( f^{\prime }/g^{\prime }\right) g-f$, we easily prove…
In the paper, concerning a question of Yi [23], we study general criterion for the uniqueness of an L-function and a general meromorphic function. Our results improve and extend all the existing results in this direction [23, 18, 17, 4] to…
We study singular solutions to the fractional Laplace equation and, more generally, to nonlocal linear equations with measurable kernels. We establish B\^ocher type results that characterize the behavior of singular solutions near the…
In this paper, we prove a conditional limit theorem for independent not necessarily identically distributed random variables. Namely, we obtain the asymptotic distribution of a large number of them given the sum.
We establish bounds for the covariance of a large class of functions of infinite variance stable random variables, including unbounded functions such as the power function and the logarithm. These bounds involve measures of dependence…
In this paper, we give a more physical proof of Liouville's theorem for a class generalized harmonic functions by the method of parabolic equation.
The paper concerns the solvability by quadratures of linear differential systems, which is one of the questions of differential Galois theory. We consider systems with regular singular points as well as those with (non-resonant) irregular…
We prove omega results for the central value of $L$-functions with the further condition that the angle is also constrained.
This article provides several theorems regarding the existence of limit for multivariable function, among which Theorem 1 and Theorem 3 relax the requirement for sequence of Heine's definition of limit. These results address the question of…
We consider the problem of deciding whether a common solution to a multivariate polynomial equation system is isolated or not. We present conditions on a given truncated Puiseux series vector centered at the point ensuring that it is not…
The uniqueness question of the multivariate moment problem is studied by different methods: Hilbert space operators, complex function theory, polynomial approximation, disintegration, integral geometry. Most of the known results in the…
We establish a coupled fixed points theorem for a meaningful class of mixed monotone multivalued operators and then we use it to derive some results on existence of quasisolutions and solutions to first--order functional differential…
The purpose of this paper is to present some multidimensional fixed-point theorems and their applications. For this, we provide a multidimensional fixed point theorem and then using this theorem we prove the existence and uniqueness of a…
We prove a general functional limit theorem for multiparameter fractional Brownian motion. The functional law of the iterated logarithm, functional L\'{e}vy's modulus of continuity and many other results are its particular cases.…