Landau-type Inequalities Research Articles

Korneichuk-Stechkin Lemma, Ostrowski and Landau Inequalities, and Optimal Recovery Problems for L-Space Valued Functions

We prove an analogue of the Korneichuk–Stechkin lemma for functions with values in L-spaces. As applications, we obtain sharp Ostrowski type inequalities and solve problems of optimal recovery of identity and convexifying operators, as well as the problem of integral recovery on the classes of L-space valued functions with given majorant of modulus of continuity. The recovery is done based on n mean values of the functions over intervals. Moreover, on the classes of functions with given majorant of modulus of continuity of their Hukuhara type derivative, we solve the problem of optimal recovery of the function and the Hukuhara type derivative. The recovery is done based on n values of the function. We obtain sharp Landau type inequalities and solve an analogue of the Stechkin problem about approximation of unbounded operators by bounded ones and the problem of optimal recovery of an unbounded operator on a class of elements, known with error. Consideration of L-space valued functions gives a unified approach to solution of the mentioned above extremal problems for the classes of multi- and fuzzy-valued functions, and for the classes of functions with values in Banach spaces, in particular random processes, and many other classes of functions.

Multivariate Caputo left fractional Landau inequalities

Abstract Relied on author’s first ever found multivariate Caputo fractional Taylor’s formula (2009, [1], Chapter 13), we develop and prove several multivariate left side Caputo fractional uniform Landau type inequalities.

One-Dimensional Interpolation Inequalities, Carlson–Landau Inequalities, and Magnetic Schrödinger Operators

In this paper we prove refined first-order interpolation inequalities for periodic functions and give applications to various refinements of the Carlson--Landau-type inequalities and to magnetic Schrodinger operators. We also obtain Lieb-Thirring inequalities for magnetic Schrodinger operators on multi-dimensional cylinders.

Landau type inequalities for Banach space valued functions

Motivated by the work of George A. Anastassiou in (George A. Anastassiou, Os- trowski and Landau inequalities for Banach space valued functions, Mathematical and Computer Modelling, 55 (2012), 312-329), we derive some Landau type inequalities for Banach space val- ued functions without assuming the boundary conditions.

Mixed Caputo fractional Landau inequalities

Here we establish mixed Caputo fractional ‖ . ‖ p , Landau type inequalities, p ∈ ( 1 , ∞ ] . We give applications on R .

Left Caputo fractional [formula omitted]-Landau inequalities

Here we establish left Caputo fractional ‖ ⋅ ‖ ∞ -Landau type inequalities. We give applications and we recover the original Landau inequality on R + .

Some Landau type inequalities for functions whose derivatives are of locally bounded variation

Some inequalities of the Landau type for functions whose derivatives are of locally bounded variation are pointed out.

Landau-type inequalities and -bounded solutions of neutral delay systems

Landau-type inequalities and -bounded solutions of neutral delay systems

Landau's Type Inequalities

LetXbe a complex Banach space, and lett→T(t) (‖T(t)‖≤1,t≥0) be a strongly continuous contraction semigroup (onX) with infinitesimal generatorA. This paper proves that -- Formula omitted -- hold for everyx∈D(A4). Inequalities are established also for uniformly bounded strongly continuous semigroups, groups, and cosine functions.

Weighted Landau-type inequalities

Landau-type inequalities are investigated with general weight functions satisfying appropriate conditions.

Some Landau's type inequalities for infinitesimal generators

Lett ↦ T(t) be a strongly continuous contraction semigroup on a complex Banach space and letA be its infinitesimal generator. We prove that, forx ∈D(A3), the following inequalities hold true: ∥Ax∥3 ⩽ 243/8 ∥x∥2∥A3x∥, ∥A2x∥ ⩽ 24 ∥x∥∥A3x∥2. Ift → T(t) is a contraction group (resp. cosine function) we get the analogous but better inequalities with constants 9/8 and 3 (resp. 81/40 and 72/25) instead of 243/8 and 24. We consider also uniformly bounded semigroups, groups and cosine functions.

Landau-type inequalities for functions defined on a bounded interval. Application to functions of several variables

Landau-type inequalities for functions defined on a bounded interval. Application to functions of several variables

Landau-type inequalities for bounded intervals

Landau-type inequalities for bounded intervals

Landau-type inequalities for some linear differential operators

Landau-type inequalities for some linear differential operators