Related papers: An Integral Inequality and the Riccati-Bernoulli D…
In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.
The aim of the present paper is to study the existence, uniqueness and some other properties of solutions of a certain partial dynamic integrodifferential equations. The Banach fixed point theorem and certain fundamental inequality with…
Classical Lie group theory provides a universal tool for calculating symmetry groups for systems of differential equations. However Lie's method is not as much effective in the case of integral or integro-differential equations as well as…
In this paper we present a special formula for transforming integrals to series. The resulting series involves binomial transforms with the Taylor coefficients of the integrand. Five applications are provided for evaluating challenging…
We give an efficient algorithm which can obtain a relative error approximation to the spectral norm of a matrix, combining the power iteration method with some techniques from matrix reconstruction which use random sampling.
This paper is concerned with the study of the fractional finite sums theory. We present the classes of functions for which it is possible to characterize the constant related to the derivative of fractional sums (denominated by essence of a…
We consider several possible approaches to evaluating an integral involving the digamma function and a related logarithmic series.
We describe partial differential operators for which we can construct generalised integral means satisfying Pizzetti-type formulas. Using these formulas we give a new characterisation of summability of formal power series solutions to some…
We study Betti numbers of sequences of Riemannian manifolds which Benjamini-Schramm converge to their universal covers. Using the Price inequalities we developed elsewhere, we derive two distinct convergence results. First, under a negative…
In this paper, we derive a Reilly formula for differential forms on weighted manifolds with nonempty boundary. As an application of this formula, we prove a Poincar\'e-type inequality in the same context and explore several of its…
Power series in which the summand satisfies a linear recurrence relation with polynomial coefficients are shown to be the solution of a linear differential or algebraic equation. Solving the associated differential or algebraic equation…
We establish deviation inequalities for the maxima of partial sums of a martingale differences sequence, and of a strictly stationary orthomartingale random field. These inequalities can be used to establish complete convergence of…
By using the associated and restricted Stirling numbers of the second kind, we give some generalizations of the poly-Bernoulli numbers. We also study their arithmetical and combinatorial properties. As an application, at the end of the…
Inequalities play an important role in pure and applied mathematics. In particular, Opial inequality plays a main role in the study of the existence and uniqueness of initial and boundary value problems for differential equations. It has…
N. Kishore, Proc. Amer. Math. Soc. 14 (1963), 523, considered the Rayleigh functions sigma_n, sums of the negative even powers of the (non-zero) zeros of the Bessel function J_nu(z) and provided a convolution type sum formula for finding…
The purpose of this article is to present closed forms for various types of infinite series involving Fibonacci (Lucas) numbers and the Riemann zeta function at integer arguments.
We systematically analyze the nonlinear partial differential equation that determines the behaviour of a bounded radiating spherical mass in general relativity. Four categories of solution are possible. These are identified in terms of…
These notes aim to provide a classical approach to solving some conformable differential equations based on prior knowledge of how to solve ordinary differential equations. That is, using the methods of separation of variables, homogeneous…
We consider the sum $\sum 1/\gamma$, where $\gamma$ ranges over the ordinates of nontrivial zeros of the Riemann zeta-function in an interval $(0,T]$, and consider the behaviour of the sum as $T \to\infty$. We show that, after subtracting a…
Let $n$ be a positive integer and let $0 < \alpha < n.$ In this paper, we continue our study of the integral equation $$ u(x) = \int_{R^{n}} \frac{u(y)^{(n+\alpha)(n-\alpha)}{|x - y|^{n-\alpha}}dy.$$ We mainly consider singular solutions in…