In this work, an improvement of Hölder–McCarty inequality is established. Based on that, several refinements the generalized mixed Schwarz are obtained. Consequently, some new numerical radius inequalities proved. New for $$n\times n$$ matrix Hilbert space operators proved as well. Some earlier results were in literature also given. presented refined and it shown to be better than literature.

The paper is devoted to the study of mappings satisfying inverse Poletsky inequality. We local behavior these mappings. are most interested in case when corresponding majorant integrable on some set spheres positive linear measure. Our main result a logarithmic Hölder continuity such at inner points. As corollary, we have established existence continuous ACL-solution Beltrami equation, which co...

The article investigates the local and boundary behavior of mappings with branching that satisfy inverse inequality Poletsky type. It is proved this type are logarithmically Hölder-continuous under condition function Q responsible for a distortion modulus families curves integrable. A continuous extension indicated to obtained. In addition, conditions which mentioned equicontinuous inside domai...

We prove in this paper the global Lorentz estimate term of fractional-maximal function for gradient weak solutions to a class p-Laplace elliptic equations containing non-negative Schrödinger potential which belongs reverse Hölder classes. In particular, operator includes both degenerate and non-degenerate cases. The interesting idea is use an efficient approach based on level-set inequality rel...

In this paper we study the regularity of weak solutions to an elliptic-parabolic system modeling natural network formation. The is singular and involves cubic nonlinearity. Our investigation reveals that are Hölder continuous when space dimension N 2. This achieved via inequality associated with Stummel-Kato class functions refinement a lemma originally due S. Campanato C.B. Morrey ([5], p. 86).

We prove new Hardy–Copson-type (γ,a)-nabla fractional dynamic inequalities on time scales. Our results are proven by using Keller’s chain rule, the integration parts formula, and Hölder inequality When γ=1, then we obtain some well-known time-scale due to Hardy. As special cases, continuous discrete inequalities. Symmetry plays an essential role in determining correct methods solve

An example of an activation function $$\sigma $$ is given such that networks with activations $$\{\sigma , \lfloor \cdot \rfloor \}$$ integer weights and a fixed architecture depending only on the input dimension d approximate continuous functions $$[0,1]^d$$ . The range required for $$\varepsilon -approximation Hölder derived, which, together our discrete choice weights, allows to obtain numbe...

The story begins with the paper of Müller, [59], who — for the sake of an application to nonlinear elasticity — proved that if the Jacobian determinant Ju of a Sobolev map u ∈ W 1,n loc (Rn ,Rn ) is nonnegative, then it belongs locally to L log L. The result is quite intriguing, since a priori Hölder inequality implies only that Ju ∈ L1 and one does not suspect any higher integrability. If one ...