Related papers: Approximation by multivariate Kantorovich-Kotelnik…
Here Lq-Lp boundedness of integral operator with operator-valued kernels is studied and the main result is applied to convolution operators. Using these results Besov space regularity for Fourier multiplier operator is established.
In this article, we analyze the approximation properties of the new family of Durrmeyer type exponential sampling operators. We derive the point-wise and uniform approximation theorem and Voronovskaya type theorem for these generalized…
We study approximation by arbitrary linear combinations of $n$ translates of a single function of periodic functions. We construct some methods of this approximation for functions in a class induced by the convolution with a given function,…
We provide the most general forms of covariant and normalized time operators and their probability densities, with applications to quantum clocks, the time of arrival, and Lyapunov quantum operators. Examples are discussed of the profusion…
Estimating entropy and mutual information consistently is important for many machine learning applications. The Kozachenko-Leonenko (KL) estimator (Kozachenko & Leonenko, 1987) is a widely used nonparametric estimator for the entropy of…
In this paper, we present some operator and eigenvalue inequalities involving operator monotone, doubly concave and doubly convex functions. These inequalities provide some variants of operator Acz\'{e}l inequality and its reverse via…
The present work considers two important convergence techniques, namely deferred type statistical convergence and P-summability method in respect of positive linear operators. With regard to these techniques, we state and prove two general…
Conditions for linear integral operators on $L_p$ over measure spaces to satisfy the polynomial covariance type commutation relations are described in terms of defining kernels of the corresponding integral operators. Representation by…
Kantorovich operators are non-linear extensions of Markov operators and are omnipresent in several branches of mathematical analysis. The asymptotic behaviour of their iterates plays an important role even in classical ergodic, potential…
This work deals with the functional model for a class of extensions of symmetric operators and its applications to the theory of wave scattering. In terms of Boris Pavlov's spectral form of this model, we find explicit formulae for the…
We calculate the least upper bounds of pointwise and uniform approximations for classes of $2\pi$-periodic functions expressible as convolutions of an arbitrary square summable kernel with functions, which belong to the unit ball of the…
In this note the Choquet type operators are introduced, in connection to Choquet's theory of integrability with respect to a not necessarily additive set function. Based on their properties, a quantitative estimate for the nonlinear…
A variety of techniques have been developed for the approximation of non-periodic functions. In particular, there are approximation techniques based on rank-$1$ lattices and transformed rank-$1$ lattices, including methods that use sampling…
In this paper, we prove some operator inequalities associated with an extension of the Kantorovich type inequality for $s$-convex function. We also give an application to the order preserving power inequality of three variables and find a…
The Maurey-Rosenthal theorem states that each bounded and linear operator T from a quasi normed space E into some L_p(\nu) which satisfies a certain vector-valued inequality even allows a weighted norm inequality. Continuing the work of…
Baskakov operators and their inverses can be expressed as linear differential operators on polynomials. Recurrence relations are given for the computation of these coefficients. They allow the construction of the associated Baskakov…
In the present paper, we introduce Stancu-variant of generalized Baskakov operators and study the rate of convergence using modulus of continuity, order of approximation for the derivative of function f . Direct estimate is proved using…
In terms of the best approximations of functions and generalized moduli of smoothness, direct and inverse approximation theorems are proved for Besicovitch almost periodic functions whose Fourier exponent sequences have a single limit point…
Quasi-symmetric functions show up in an approach to solve the Kadomtsev-Petviashvili (KP) hierarchy. This moreover features a new nonassociative product of quasi-symmetric functions that satisfies simple relations with the ordinary product…
The connection between derivative operators and wavelets is well known. Here we generalize the concept by constructing multiresolution approximations and wavelet basis functions that act like Fourier multiplier operators. This construction…