Related papers: Revisiting the Gr\"uss Inequality
In this article, we proved upper bounds for numerical radius of bounded linear operator and product of operators which generalize and improve existing inequalities. We also obtain a numerical radius inequality of invertible operator using…
In this article, we present some new general forms of numerical radius inequalities for Hilbert space operators. The significance of these inequalities follow from the way they extend and refine some known results in this field. Among other…
In this article, we present several inequalities treating operator means and the Cauchy-Schwarz inequality. In particular, we present some new comparisons between operator Heron and Heinz means, several generalizations of the difference…
In this article, we obtain several new weighted bounds for the numerical radius of a Hilbert space operator. The significance of the obtained results is the way they generalize many existing results in the literature; where certain values…
In this paper, some new Gronwall type inequalities involving iterated integrals are given.
We study functional inequality of the form $$|T(f,h)-T(f,g)T(g,h)| \leq F(f,g)F(g,h) -F(f,h)$$ where $T$ is a complex-valued functional and $F$ is a real-valued map. Motivation for our studies comes from some generalizations of Gr\"uss…
We establish new integral inequalities for the numerical radius and the operator norm of bounded linear operators on Hilbert spaces. Our results refine classical triangle-type and operator matrix inequalities by incorporating convex…
In this short paper we show that the inequality of arithmetic and geometric means is reduced to another interesting inequality, and a proof is provided.
In this paper, we study the existence of solutions of some kinds of operator equations via operator inequalities. First, we investigate characterizations of operator order $A\geqslant B >0$ and chaotic operator order log $A \geqslant$ log…
In this paper, we present several new bounds for the norm and numerical radius of sums of Hilbert space operators. The obtained bounds form a new collection that enriches our understanding of these bounds. We compare our bounds with the…
The weighted numerical radius of a Hilbert space operator has been defined recently. This article explores other properties and uses this newly defined numerical radius to obtain several new interesting inequalities for the weighted…
This paper is devoted to a systematic study of certain geometric integral inequalities which arise in continuum combinatorial approaches to $L^p$-improving inequalities for Radon-like transforms over polynomial submanifolds of intermediate…
In this work, some generalizations and refinements inequalities for numerical radius of the product of Hilbert space operators are proved. New inequalities for numerical radius of block matrices of Hilbert space operators are also…
In this article, we focus on establishing a new variant of Hermite-Hadamard type inequalities for operator convex maps using an appropriate probability measure. To underline the usefulness of these inequalities, we investigate some…
In \cite{PSMA}, Pal et al. introduced some weighted means and gave some related inequalities by using an approach for operator monotone functions. This paper discusses the construction of these weighted means in a simple and nice setting…
In this paper we present some inequalities involving operator decreasing functions and operator means. These inequalities provide some reverses of operator Acz\'el inequality dealing with the weighted geometric mean.
We introduce a new approach to the spectral equivalence of Gaussian processes and fields, based on the methods of operator theory in Hilbert space. Besides several new results including identities in law of quadratic norms for integrated…
In this paper we obtain some new refinements and reverses of Young's operator inequality. Extensions for convex functions of operators are also provided.
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…
The classical form of Gr\"{u}ss' inequality was first published by G. Gr\"{u}ss in 1935 and gives an estimate of the difference between the integral of the product and the product of the integrals of two functions. After that many variants…