Related papers: Bounding the Cebysev Functional for Sequences of V…

We obtain some new inequalities of Chebyshev Type.

This paper deals with a class of Sobolev spaces of vector-valued functions on a compact group. Some Sobolev embedding theorems are proved.

In this work, considering a general subclass of bi-univalent functions and using the Chebyshev polynomials, we obtain coefficient expansions for functions in this class.

Recently the theory of widths of Kolmogorov (especially of Gelfand widths) has received a great deal of interest due to its close relationship with the newly born area of Compressed Sensing. It has been realized that widths reflect properly…

We establish an $\varepsilon$-regularity result for the derivative of a map of bounded variation that minimizes a strongly quasiconvex variational integral of linear growth, and, as a consequence, the partial regularity of such BV…

We define and study the vanishing sequence along a real valuation of sections of a line bundle on a projective variety. Building on previous work of the first author with Huayi Chen, we prove an equidistribution result for vanishing…

In this paper, a new lemma is proved and inequalities of Simpson type are established for co-ordinated convex functions and bounded functions.

In this work, generalizations of some inequalities for continuous $h$-synchronous ($h$-asynchronous) functions of linear bounded selfadjoint operators under positive linear maps in Hilbert spaces are proved.

Some sharp inequalities of Gruss type for sequences of vectors in real or complex normed linear spaces are obtained. Applications for the discrete Fourier and Mellin transform are given. Estimates for polynomials with coefficients in normed…

We present weighted Sobolev spaces and prove a trace theorem for the spaces. As an application, we discuss non-zero boundary value problems for parabolic equations. The weighted parabolic Sobolev spaces we consider are designed, in…

We study fractional Sobolev and Besov spaces on noncompact Riemannian manifolds with bounded geometry. Usually, these spaces are defined via geodesic normal coordinates which, depending on the problem at hand, may often not be the best…

A quasi-product on the normed space is defined. In addition, the notions of the eigenvectors of a linear operator can be extended for the nonlinear operator. Based on the quasi-product and the generalized eigenvectors, the spectral theorems…

We study central limit theorems for certain nonlinear sequences of random variables. In particular, we prove the central limit theorems for the bounded conductivity of the random resistor networks on hierarchical lattices.

We investigate metric projections and distance functions referring to convex bodies in finite-dimensional normed spaces. For this purpose we identify the vector space with its dual space by using, instead of the usual identification via the…

Among other results, the paper gives new mapping theorems and new fixed point property theorems for inverse limits of inverse sequences of compact metric spaces with upper semicontinuous set-valued bonding functions. We also revisit the…

Restricted non-linear approximation is a type of N-term approximation where a measure $\nu$ on the index set (rather than the counting measure) is used to control the number of terms in the approximation. We show that embeddings for…

Covariant Lyapunov vectors (CLVs) are intrinsic modes that describe long-term linear perturbations of solutions of dynamical systems. With recent advances in the context of semi-invertible multiplicative ergodic theorems, existence of CLVs…

Let a vector-valued sublinear operator satisfy the size condition and be bounded on weighted Lebesgue spaces with variable exponent. Then we obtain its boundedness on weighted grand Herz-Morrey spaces with variable exponents. Next we…

In this paper we deal with the convergence of sequences of positive linear maps to a (not assumed to be linear) isometry on spaces of continuous functions. We obtain generalizations of known Korovkin-type results and provide several…

In this report, we consider extended real-valued functions on some real vector space. Gerstewitz functionals are used to construct all translative functions. We derive formulas for translative functions which are lower semicontinuous,…