Related papers: An Integral Inequality and the Riccati-Bernoulli D…
We introduce a new system of split variational inequality problems which is a natural extension of split variational inequality problem in semi-inner product spaces. We use the retraction technique to propose an iterative algorithm for…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
In this paper, we obtain some inequalities by using a kernel and an inequality which is a result of Young inequality. Besides we give some applications to special means.
A spectral decomposition method is used to obtain solutions to a class of nonlinear differential equations. We extend this approach to the analysis of the fractional form of these equations and demonstrate the method by applying it to the…
We give an expression of polynomials for higher sums of powers of integers via the higher order Bernoulli numbers.
In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…
Some twenty years ago we introduced a nonstandard matrix Riccati equation to solve the partial stochastic realization problem. In this paper we provide a new derivation of this equation in the context of system identification. This allows…
Comparison of approximate solutions that were obtained by using different asymptotic methods of solutions of difference equations with the exact solution is presented. Results show that for the studied equation the method of transformation…
We provide a general theorem for evaluating trigonometric Dirichlet series of the form $\sum_{n \geq 1} \frac{f (\pi n \tau)}{n^s}$, where $f$ is an arbitrary product of the elementary trigonometric functions, $\tau$ a real quadratic…
In this paper, we propose a numerical method of computing Hadamard finite-part integrals with an integral power singularity at the endpoint on a half infinite interval, that is, a finite value assigned to a divergent integral with an…
In this paper, we obtain some new results about weakly singular integral inequalities. These inequalities are used to discuss the global existence and uniqueness results for fractional differential equations of Riemann-Liouville type. Some…
We give the rate of convergence of some optimal lower Riemann-Stieltjes sums toward the integral.
We provide algorithms computing power series solutions of a large class of differential or $q$-differential equations or systems. Their number of arithmetic operations grows linearly with the precision, up to logarithmic terms.
In this paper we present a new approach to proving some exponential inequalities involving the sinc function. Power series expansions are used to generate new polynomial inequalities that are sufficient to prove the given exponential…
Matrix Riccati differential equations arise in many different areas and are particular important within the field of control theory. In this paper we consider numerical integration for large-scale systems of stiff matrix Riccati…
In our recent paper we gave an efficient algorithm to calculate "small" solutions of relative Thue equations (where "small" means an upper bound of type $10^{500}$ for the sizes of solutions). Here we apply this algorithm to calculating…
In this paper, we propose a numerical method of computing an Hadamard finite-part integral, a finite value assigned to a divergent integral, with a non-integral power singularity at the endpoint on a half infinite interval. In the proposed…
An interplay between the sum of certain series related to Harmonic numbers and certain finite trigonometric sums is investigated. This allows us to express the sum of these series in terms of the considered trigonometric sums, and permits…
In this article we present a new recurrence formula for a finite sum involving the Fibonacci sequence. Furthermore, we state an algorithm to compute the sum of a power series related to Fibonacci series, without the use of term-by-term…
In this paper we propose a method for proving some exponential inequalities based on power series expansion and analysis of derivations of the corresponding functions. Our approach provides a simple proof and generates a new class of…