We consider the class of integral operators Qφ on L (R+) of the form (Qφf)(x) = ∫ ∞ 0 φ(max{x, y})f(y)dy. We discuss necessary and sufficient conditions on φ to insure that Qφ is bounded, compact, or in the Schatten–von Neumann class Sp, 1 < p < ∞. We also give necessary and sufficient conditions for Qφ to be a finite rank operator. However, there is a kind of cut-off at p = 1, and for membersh...

*Correspondence: [email protected] 1Department of Mathematics and Computer Science, Wuyi University, Wuyishan, 354300, China Full list of author information is available at the end of the article Abstract In this paper, a kind of Schurer type q-Bernstein-Kantorovich operators is introduced. The Korovkin type approximation theorem of these operators is investigated. The rates of convergence of ...

In 1995, Yudovich extended his own 1963 uniqueness result for solutions to the 2D Euler equations with bounded initial vorticity to allow a certain class of initial vorticities whose L-norms grow no faster than roughly log p. Yudovich’s argument involves estimating part of the difference between two velocities in terms of the L∞-norm of each velocity. Because the two velocities have a (common) ...

In the present paper, we study some approximation properties of a modified Jain-Gamma operator. Using Korovkin type theorem, first give such Secondly, compute rate convergence this operator by means modulus continuity and weighted spaces. Finally, obtain Voronovskaya theorem

This paper is concerned with functional variations in processes associatedwith Continuous Flow Models (CFMs). The considered CFMs are character-ized (defined) by their inflow-rate process, service-rate process, and buffer size,and have associated with them various derived processes such as the workload(buffer contents), outflow and overflow processes. The paper’s main result is<...

The regularization of linear ill-posed problems is based on their conditional well-posedness when restricting the problem to certain classes of solutions. Given such class one may consider several related real-valued functions, which measure the well-posedness of the problem on such class. Among those functions the modulus of continuity is best studied. For solution classes which enjoy the addi...

R.P. Boas has found necessary and sufficient conditions of belonging of function to Lipschitz class. From his findings it turned out, that the conditions on sine and cosine coefficients for belonging of function to Lip α (0 < α < 1) are the same, but for Lip 1 are different. Later his results were generalized by many authors in the viewpoint of generalization of condition on the majorant of mod...

In the present paper we give quantitative type theorems for differences of different bivariate positive linear operators by using weighted modulus continuity. Similar estimates are obtained via K-functional and Chebyshev functionals. Moreover, an example involving Szasz Szasz-Kantorovich is given.

We discuss various properties of the new modulus of smoothness ω k,r (f, t)p := sup 0<h6t ‖W kh(·)∆khφ(·)(f , ·)‖Lp [−1,1], where φ(x) := √ 1− x2 and Wδ(x) = ( (1−x−δφ(x)/2)(1+x−δφ(x)/2) )1/2 . Related moduli with more general weights are also considered.

In the present article, we construct Szász-Jakimovski-Leviatan operators in parametric form by including sequences of continuous functions and then investigate approximation properties. We have successfully estimated convergence use modulus continuity spaces Lipschitz functions, Peetres $ K $-functional weighted functions.