arXiv subjects

Fahreddin Abdullayev

Publications and source records attributed to Fahreddin Abdullayev.

5 recordsLinked to original sources

arXiv2020

Widths of functional classes defined by majorants of generalized moduli of smoothness in the spaces ${\mathcal S}^p$

Exact Jackson-type inequalities are obtained in terms of best approximations and averaged values of generalized moduli of smoothness in the spaces ${\mathcal S}^p$. The values of Kolmogorov, Bernstein, linear, and projective widths in the spaces ${\mathcal S}^p$ are found for classes of periodic functions defined by certain conditions on the averaged values of the generalized moduli of smoothness.

math.CA↗

arXiv2020

Direct and inverse approximation theorems of functions in the Musielak-Orlicz type spaces

In Musilak-Orlicz type spaces ${\mathcal S}_{\bf M}$, direct and inverse approximation theorems are obtained in terms of the best approximations of functions and generalized moduli of smoothness. The question of the exact constants in Jackson-type inequalities is studied.

math.CA↗

arXiv2019

Direct and inverse approximation theorems of functions in the Orlicz type spaces S_M

In the Orlicz type spaces ${\mathcal S}_{M}$, we prove direct and inverse approximation theorems in terms of the best approximations of functions and moduli of smoothness of fractional order. We also show the equivalence between moduli of smoothness and Peetre $K$-functionals in the spaces ${\mathcal S}_{M}$.

math.CA↗

arXiv2012

Tangent metric spaces to starlike sets on the plane

Let $A\subseteq\mathbb C$ be a starlike set with a center $a$. We prove that every tangent space to $A$ at the point $a$ is isometric to the smallest closed cone, with the vertex $a$, which includes $A$. A partial converse to this result is obtained. The tangent space to convex sets is also discussed.

math.MG↗

arXiv2009

Metric spaces with unique pretangent spaces

We find necessary and sufficient conditions under which an arbitrary metric space $X$ has a unique pretangent space at the marked point $a\in X$. Key words: Metric spaces; Tangent spaces to metric spaces; Uniqueness of tangent metric spaces; Tangent space to the Cantor set.

math.MG↗