Related papers: Some companions of perturbed Ostrowski type inequa…
This paper is devoted to the study of the singularly perturbed second order partial integro-differential equations. The estimation of the solutions of Cauchy problem is obtained.
We prove generalized weighted Ostrowski and Ostrowski--Gr\"uss type inequalities on time scales via a parameter function. In particular, our result extends a result of Dragomir and Barnett. Furthermore, we apply our results to the…
In this paper, some new Gronwall type inequalities involving iterated integrals are given.
We first prove some weighted inequalities for compositions of functions on time scales which are in turn applied to establish some new dynamic Opial-type inequalities in several variables. Some generalizations and applications to partial…
Some selected Ostrowski type inequalities and a connection with numerical integration are studied in this survey paper, which is dedicated to the memory of Professor D.S. Mitrinovic, who left us 25 years ago. His significant influence to…
In this paper, we introduce and investigate a new subclass of bi-prestarlike functions defined in the open unit disk, associated with Chebyshev Polynomials. Furthermore, we find estimates of first two coefficients of functions in these…
In this paper, we obtain some Simpson type inequalities for functions whose second derivatives absolute value or q-th power of them are Q-class functions. Also we give applications to numerical integration.
In this study, linear second-order conformable differential equations using a proportional derivative are shown to be formally self-adjoint equations with respect to a certain inner product and the associated self-adjoint boundary…
We extend the Moser-Trudinger inequality of one function to systems of orthogonal functions. Our results are asymptotically sharp when applied to the collective behavior of eigenfunctions of Schr\"odinger operators on bounded domains.
This is a continuation of our papers \cite{AP2} and \cite{AP3}. In those papers we obtained estimates for finite differences $(\D_Kf)(A)=f(A+K)-f(A)$ of the order 1 and $(\D_K^mf)(A)\df\sum\limits_{j=0}^m(-1)^{m-j}(m\j)f\big(A+jK\big)$ of…
We consider perturbations of the non-unitary minimal model solutions of two-dimensional conformal turbulence proposed by Polyakov. Demanding the absence of non-integrable singularities in the resulting theories leads to constraints on the…
Stochastic partial differential equations of second order with two unknown parameters are studied. Based on ergodicity, two suitable families of minimum constrast estimators are introduced. Strong consistency and asymptotic normality of…
We present new criteria for the existence of oscillatory and nonoscillatory solutions of measure delay differential equations with impulses. We deal with the integral forms of the differential equations using the Perron and the…
We study the behaviour of functions of pairs of commuting self-adjoint operators under perturbations by relatively bounded operators. We obtain analogs of our earlier results for functions of a single self-adjoint operator under relatively…
We show that Green functions of second-order differential operators with singular or unbounded coefficients can have an anomalous behaviour in comparison to the well-known properties of Green functions of operators with bounded…
Several families of sharp Bernstein inequalities are established on the weighted $L^2$ space over parabolic domains, which include bounded or unbounded rotational paraboloids and parabolic surfaces. The main tool is a second-order…
We consider semiclassical orthogonal polynomials on the unit circle associated with a weight function that satisfy a Pearson-type differential equation involving two polynomials of degree at most three. Structure relations and difference…
Based on the gauge invariant variables proposed in our previous paper [K. Nakamura, Prog. Theor. Phys. vol.110 (2003), 723.], some formulae of the perturbative curvatures of each order are derived. We follow the general framework of the…
In the paper, the authors establish some new Hermite-Hadamard type inequalities for functions whose first derivatives are of convexity and apply these inequalities to construct inequalities of special means.
Perturbation bounds for Mostow's decomposition and the bipolar decomposition of matrices have been computed. To do so, expressions for the derivative of the geometric mean of two positive definite matrices have been derived.