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On Iterated Discrete Hardy Type Inequalities for a Class of Matrix Operators
In this paper, we discuss new iterated discrete inequalities of Hardy type involving matrix kernels. Under some conditions on matrix entries of the...
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Hardy–Sobolev Inequalities For Riesz Potentials Of Functions In Orlicz Spaces
We establish a Hardy–Sobolev inequality for Riesz potentials of functions in Orlicz spaces.
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Some Hermite–Hadamard type inequalities for functions of generalized convex derivative
We obtain some new inequalities of Hermite–Hadamard type. We consider functions that have convex or generalized convex derivative. Additional...
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Complete Monotonicity for a New Ratio of Finitely Many Gamma Functions
In this paper, by deriving an inequality involving the generating function of the Bernoulli numbers, the author introduces a new ratio of finitely...
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Random sampling of signals concentrated on compact set in localized reproducing kernel subspace of \(L^p(\mathbb R^n)\)
The paper is devoted to studying the stability of random sampling in a localized reproducing kernel space. We show that if the sampling set on
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Rearrangement and the weighted logarithmic Sobolev inequality
Here we consider some weighted logarithmic Sobolev inequalities which can be used in the theory of singular Riemannian manifolds. We give the...
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Banach Spaces and Inequalities Associated with New Generalization of Cesàro Matrix
Let the triangle matrix A ru be a generalization of the Cesàro matrix and U ∈ { c 0 , c, ℓ ∞ }. In this study, we essentially deal with the space U ( A ru )...
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p-Capacity with Bessel Convolution
We define and examine nonlinear potential by Bessel convolution with Bessel kernel. We investigate removable sets with respect to Laplace-Bessel...
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Brezis–Marcus Problem and its Generalizations
Certain Hardy inequalities in domains of Euclidean space contain sharp but unreachable constants. V. G. Maz’ya and other authors used this fact to...
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Finsler Trudinger-Moser inequalities on ℝ2
The first aim of this article is to study the sharp singular (two-weight) Trudinger-Moser inequalities with Finsler norms on ℝ 2 . The second goal is...
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Hardy and Rellich type inequalities with remainders
Hardy and Rellich type inequalities with an additional term are proved for compactly supported smooth functions on open subsets of the Euclidean...
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On q-Hermite–Hadamard inequalities for general convex functions
The Hermite–Hadamard inequality was first considered for convex functions and has been studied extensively. Recently, many extensions were given with...
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New Hardy-type integral inequalities
The proofs of generalized Hardy, Copson, Bennett, Leindler-type, and Levinson integral inequalities are revisited. It is contemplated to establish...
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An extension of the Hermite–Hadamard inequality for convex and
s -convex functionsThe Hermite–Hadamard inequality was extended using iterated integrals by Retkes [Acta Sci Math (Szeged) 74:95–106,
2008 ]. In this paper we further... -
(0, 0)-Convex Functions and Their Properties
We introduce the concept of ( α, β )-convex function on an interval. We study in detail the properties of the (0 , 0)-convex functions and their...
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Inequalities Involving Fractional Integrals of a Function and Its Derivative
New inequalities for fractional integrals of a function and its derivative are proved. Lower estimates of weighted norms of the derivative through...
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Generalization of the Quotient Mean Series
In this paper a new family of generalized Mathieu series, called Quotient mean Matheu series is introduced. Namely, some generalized Mathieu series,...
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Functionals Related to Gauss–Pólya Type Inequalities Involving Derivatives
We consider several functionals associated with inequalities which involve derivatives of functions. As a consequence of those results we get new...