Related papers: The Bohr inequality for the generalized C{\'e}saro…
In this paper, we apply techniques from equivariant geometry to prove that a generalized Bour's theorem holds for surfaces that are invariant under the action of a one-parameter group of isometries of a three-dimensional Riemannian…
A generalization of the H\"older inequality is considered. Its relations with a previously obtained improvement of the Cauchy--Schwarz inequality are discussed.
In this article, we first establish operator-valued analogues of multidimensional refined Bohr inequality. Then we establish operator-valued analogues of multidimensional improved Bohr inequality with a certain power of the norm of the…
In this paper, by a concise and elementary approach, we sharpen and generalize Shafer's inequality for the arc sine function, and some known results are extended and generalized.
We develop a theory of extrapolation for weights that satisfy a generalized reverse H\"older inequality in the scale of Orlicz spaces. This extends previous results by Auscher and Martell [2] on limited range extrapolation. As an…
The purpose of this paper is to generalize a very famous result on products of normal operators, due to I. Kaplansky. The context of generalization is that of bounded hyponormal and unbounded normal operators on complex separable Hilbert…
The original Choi-Davis-Jensen's inequality, with its wide-ranging applications in diverse scientific and engineering fields, has motivated researchers to explore generalizations. In this study, we extend Davis-Choi-Jensen's inequality by…
In this paper, we prove Newton-Maclaurin type inequalities for functions obtained by linear combination of two neighboring primary symmetry functions, which is a generalization of the classical Newton-Maclaurin inequality.
In this work, a generalization of pre-Gr\"{u}ss inequality is established. Several bounds for the difference between two \v{C}eby\v{s}ev functional are proved.
For given set of $m$ positive numbers satisfying the conditions: $$ a_1 \geq a_2 \geq , ... \geq a_m \geq 0, $$ the inequality $$ \sum_{s=1}^{m} (-1)^{s-1}a^r_s \geq \left[ \sum_{s=1}^{m} (-1)^{s-1}a_s\right]^r, \quad r > 1, $$ was proved…
We extend the well-known Katznelson-Tzafriri theorem, originally posed for power-bounded operators, to the case of Ces\`aro bounded operators of any order $\alpha>0.$ For this purpose, we use a functional calculus between a new class of…
The following extension of Bohr's theorem is established: If a somewhere convergent Dirichlet series $f$ has an analytic continuation to the half-plane $\mathbb{C}_\theta = \{s = \sigma+it\,:\, \sigma>\theta\}$ that maps $\mathbb{C}_\theta$…
We develop the method of averaging in Clifford (geometric) algebras suggested by the author in previous papers. We consider operators constructed using two different sets of anticommuting elements of real or complexified Clifford algebras.…
The classical inequality of Bohr asserts that if a power series converges in the unit disk and its sum has modulus less than or equal to $1$, then the sum of absolute values of its terms is less than or equal to $1$ for the subdisk…
In this note we prove a general version of the Extrapolation Theorem, extending the classical linear extrapolation theorem due to B. Maurey. Our result shows, in particular, that the operators involved do not need to be linear.
In this paper, using a fractional integral as proposed by Katugampola we establish a generalization of integral inequalities of Gruss-type. We prove two theorems associated with these inequalities and then immediately we enunciate and prove…
In this paper we introduce two new generalized variational inequalities, and we give some existence results of the solutions for these variational inequalities involving operators belonging to a recently introduced class of operators. We…
The general notion of a Hausdorff-type operator with a kernel depending on an external variable is introduced and generalizations and analogs of classical results on the regularity of various summation methods are proved for the case of…
The transfer property for the generalized Browder's theorem both of the tensor product and of the left-right multiplication operator will be characterized in terms of the $B$-Weyl spectrum inclusion. In addition, the isolated points of…
Operator-valued multivariable Bohr type inequalities are obtained for: a class of noncommutative holomorphic functions, generalizing the analytic functions on the open unit disc; the noncommutative disc algebra and the noncommutative…