Integral equations arise naturally in applications of real world problems [5, 6, 7, 8]. The theory of integral equations has been well developed with the help of various tools from functional analysis, topology and fixed-point theory. The classical theory of integral equations can be generalized if one uses the Stieltjes integral with kernels dependent on one or two variables. The aim of this p...

In this paper we establish the general inequalities for diagonal and subdiagonal multipoint Padé approximants to a Stieltjes function f in terms of power expansion of f on the real line. The inequalities derived produce the best upper and lower bounds on f with respect to the given coefficients of Stieltjes series. As an example of applications sequences of upper and lower Padé bounds convergin...

In 1894 Thomas Jan Stieltjes (1856-1894) published an extremely influential paper: Recherches sur les fractions continues, Ann. Fac. Sci. Toulouse, 8, 1–122; 9, 5–47. He introduced what is now known as the Stieltjes integral with respect to an increasing function φ, the latter describing a distribution of mass (a measure μ) via the convention that the mass in an interval ]a, b] is μ(]a, b]) = φ...

We aim here at characterizing those nonnegative matrices whose inverse is an irreducible Stieltjes matrix. Specifically, we prove that any irreducible Stieltjes matrix is a resistive inverse. To do this we consider the network defined by the off-diagonal entries of the matrix and we identify the matrix with a positive definite Schrödinger operator which ground state is determined by the lowest ...

In this article, we study the oscillation of second order forced impulsive differential equation with γ-Laplacian and nonlinearities given by Riemann-Stieltjes integrals of the form

In the standard theory of delay equations, fundamental solution does not ‘live’ in state space. To eliminate this age-old anomaly, we enlarge As a consequence, lose strong continuity operators and this, turn, has as consequence that Riemann integral no longer suffices for giving meaning to variation-of-constants formula. compensate, develop Stieltjes-Pettis setting norming dual pair spaces. Par...

In the present paper we study a model of deformations for system n Stieltjes strings located along geometric graph-star with nonlinear condition at node