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On a uniform grid on the real axis, we study the Yanenko–Stechkin–Subbotin problem of extremal function interpolation in the mean in the space , , of two-way real sequences with the least value of the norm of a linear formally self-adjoint differential operator of order with constant real coefficients. In case of even , the value of the least norm in the space , , of the extremal interpolant is calculated exactly if the grid step and the averaging step are related by the inequality . [ABSTRACT FROM AUTHOR]

Extremal problems on the number of j-independent sets in uniform simple hypergraphs are studied. Nearly optimal results on the maximum number of independent sets for the class of simple regular hypergraphs and on the minimum number of independent sets for the class of simple hypergraphs with given average degree of vertices are obtained. [ABSTRACT FROM AUTHOR]

Erdős' well-known problem on the maximum absolute value of the derivative of a polynomial on a connected lemniscate is extended to the case of a rational function. Moreover, under the assumption that certain lemniscates are connected, a sharp upper bound for the absolute value of the derivative of a rational function at any point in the plane different from the poles is found. The role of the extremal function is played by an appropriate Zolotarev fraction. [ABSTRACT FROM AUTHOR]

We give the solution of the Delsarte extremal problem for even entire functions of exponential type that are Jacobi transforms and prove the uniqueness of the extremal function. The quadrature Markov formula on the half-line with zeros of the modified Jacobi function are used. [ABSTRACT FROM AUTHOR]

The article explores the estimation of the remainder in the asymptotic solution of an extremal problem which involves nonnegative trigonometric polynomials. Topics mentioned include the formula to denote the lower bound for real numbers, asymptotic relations which prove the existence of a positive absolute constant C, and the relationship between functions provided in the article.

This paper studies the structure of the singularity of Lagrangian manifolds in a neighborhood of the surface of singular extremals of second order in optimal control problems. For the Fuller classical problem, the structure of the Lagrangian manifold is explicitly constructed: it is shown that it has a singularity of conic type at the origin of coordinates. In the general case, it is proved that the Lagrangian manifold is a locally trivial fiber bundle over the surface of singular extremals with each fiber having a singularity of a similar conic type at the point of exit of the singular extremals. [ABSTRACT FROM AUTHOR]

The Grötzsch and Teichmüller well-known extremal problems for the moduli of plane doubly connected domains are extended to the case of domains on Riemann surfaces. [ABSTRACT FROM AUTHOR]

This paper deals with the continuity of the sharp constant K( T,X) with respect to the set T in the Jackson-Stechkin inequality , where E( f,L) is the best approximation of the function f ∈ X by elements of the subspace L ⊂ X, and ω is a modulus of continuity, in the case where the space L( $\mathbb{T}^d $, ℂ) is taken for X and the subspace of functions g ∈ L( $\mathbb{T}^d $, ℂ), for L. In particular, it is proved that the sharp constant in the Jackson-Stechkin inequality is continuous in the case where L is the space of trigonometric polynomials of nth order and the modulus of continuity ω is the classical modulus of continuity of rth order. [ABSTRACT FROM AUTHOR]

We consider the problem of the recovery of the kth order divided difference from a sequence given with an errorwith bounded divided difference of nth order, 0 ≤ k < n. The solution of this problem involves an extremal problem similar to that known in the continuous case as Taikov's inequality. [ABSTRACT FROM AUTHOR]

We consider the question of the solvability of an inclusion F( x, σ) ∈ A, i.e., of determining a mapping (implicit function) σ ↦ x( σ) defined on a set such that F( x( σ), σ) ∈ A for any σ from this set. Results of this kind play a key role in the different branches of analysis and, especially, in the theory of extremal problems, where they are the main tool for deriving conditions for an extremum. [ABSTRACT FROM AUTHOR]

We obtain exact values of different n-widths for classes of differentiable periodic functions in the space L2[0, 2π] satisfying the constraint , where 0 < h < ∞, 1/ r < p ≤ 2, r ∈ ℕ, and ω m( f( r); t) is the modulus of continuity of mth order of the derivative f( r)( x) ∈ L2[0, 2 π]. [ABSTRACT FROM AUTHOR]

In this paper, we consider extremal problems for numerical positive series. The terms of these series are pairwise products of the elements of two sequences, one of which is fixed and the other varies within a given set of sequences. We obtain exact solutions for a number of such problems. As one of the possible applications of the results obtained, we find solutions of some extremal problems related to best n-term approximations of periodic functions. [ABSTRACT FROM AUTHOR]

We study homology characteristics of critical values and extremals of Lipschitz functionals defined on bounded closed convex subsets of a reflexive space that are invariant under deformations. Sufficient conditions for the existence of a bifurcation point of a multivalued potential operator (the switch principle for the typical number of an extremal) are established. [ABSTRACT FROM AUTHOR]

The article discusses the Turán and Delsarte problems for periodic positive definite functions. The quantities for these problems were measured and established for rational numbers based on a theorem. The theorem is intended to get the explicit value for irrational numbers and to look the extremal function in the Turán problem.

The article discusses the extremal problem in a continuous periodic even real functions. Extremal problem have applications in the theory of functions, analytic number theory and digital signal processing. It is stated that the supposition on the form of the extremal function belongs to D. V. Gorbachev who accomplished the proof of the theorem.

We consider an extremal problem for even positive definite entire functions of exponential type with zero mean with power weight on the semiaxis. This problem is related to the multidimensional Jackson-Stechkin theorem in the space L 2(ℝn). [ABSTRACT FROM AUTHOR]

A complete characterization of the extremal subsets of Hilbert spaces, which is an infinite-dimensional generalization of the classical Jung theorem, is given. The behavior of the set of points near the Chebyshev sphere of such a subset with respect to the Kuratowski and Hausdorff measures of noncompactness is investigated. [ABSTRACT FROM AUTHOR]

The article presents a mathematical problem that uses Fourier sums to estimate simultaneous approximation of functions and their derivatives. It discusses the problem of simultaneous approximations in C of functions of class Wrr H[ω] and their derivatives by fourier sums. It adds that the numbers k1, k2.. km must be integers.