Related papers: Revisiting the Gr\"uss Inequality
The data processing inequality (DPI) is a scalar inequality satisfied by distinguishability measures on density matrices. For some distinguishability measures, saturation of the scalar DPI implies an operator equation relating the arguments…
In this paper, we improve and further generalize some Ostrowski-Gr\"uss type inequalities for the fractional integrals by using new Montogomery identities.
This paper contains a review of available methods for establishing improved interpolation inequalities on the sphere for subcritical exponents. Pushing further these techniques we also establish some new results, clarify the range of…
We give some new refinements of Heinz inequality and an improvement of the reverse Young's inequality for scalars and we use them to establish new inequalities for operators and the Hilbert-Schmidt norm of matrices. We give a uniformly and…
Unfair metrical task systems are a generalization of online metrical task systems. In this paper we introduce new techniques to combine algorithms for unfair metrical task systems and apply these techniques to obtain improved randomized…
The aim of this paper is to establish some new inequalities similar to the Ostrowski's inequalities which are more generalized than the inequalities of Dragomir and Cerone. The current article obtains bounds for the deviation of a function…
In this paper, we are interested in investigating a weighted variant of Hermite-Hadamard type inequalities involving convex functionals. The approach undertaken makes it possible to refine and reverse certain inequalities already known in…
The aim of this paper is to obtain some generalized weighted Ostrowski inequalities for differentiable mappings. Some well known inequalities can be derived as special cases of the inequalities obtained here. In addition, perturbed…
In this paper, we obtained some new Ostrowski-Gruss type inequalities contains twice differentiable functions.
We establish some new generalizations of Erd\H{o}s-Mordell inequality by adding weights to its terms. Using these generalizations, we derived strengthened versions of the original Erd\H{o}s-Mordell inequality. We also found two other…
This paper is mainly devoted to studying operator Jensen inequality. More precisely, a new generalization of Jensen inequality and its reverse version for convex (not necessary operator convex) functions have been proved. Several special…
Inequalities for exponential sums are studied. Our results improve an old result of G. Halasz and a recent result of G. Kos. We prove several other essentially sharp related results in this paper.
Deformed logarithms and their inverse functions, the deformed exponentials, are important tools in the theory of non-additive entropies and non-extensive statistical mechanics. We formulate and prove counterparts of Golden-Thompson's trace…
A review of the main fairness definitions and fair learning methodologies proposed in the literature over the last years is presented from a mathematical point of view. Following our independence-based approach, we consider how to build…
Several new improvements of the $A$-numerical radius inequalities for operators acting on a semi-Hilbert space, i.e., a space generated by a positive operator $A$, are proved. In particular, among other inequalities, we show that…
In this paper authors establish the two sided inequalities for the following two new means $$X=X(a,b)=Ae^{G/P-1},\quad Y=Y(a,b)=Ge^{L/A-1}.$$ As well as many other well known inequalities involving the identric mean $I$ and the logarithmic…
The aim of this work is to improve Wilker inequalities near the origin and {\pi}/2.
In this article, by combining appropriate refined Bohr's inequalities with some techniques concerning bounded analytic functions defined in the unit disk, we generalize and improve several Bohr type inequalities for such functions.
We introduce a concept called refinement and develop two different ways of refining metrics. By applying these methods we produce several refinements of the shortest-path distance on the collaboration graph and hence a couple new versions…
We present a new proof of the "arithmetic" large sieve inequality, starting from the corresponding "harmonic" inequality, which is based on an amplification idea. We show that this also adapts to give some new sieve inequality for modular…