Related papers: Mean value theorem for quantum integral operator w…
An inequality providing some bounds for the integral mean via Pompeiu's mean value theorem and applications for quadrature rules and special means are given.
Some Ostrowski type inequalities via Cauchy's mean value theorem and applications for certain particular instances of functions are given.
We discover a new version of the celebrated Montgomery identity via quantum integral operators and establish certain quantum integral inequalities of Ostrowski type by using this identity. Relevant connections of the results obtained in…
We disprove and correct some recently obtained results regarding Montgomery identity for quantum integral operator and Ostrowski type inequalities involving convex functions.
In this paper we derive a new inequality of Ostrowski-Gruss type on time scales and thus unify corresponding continuous and discrete versions. We also apply our result to the quantum calculus case.
The ostrowski inequality expresses bounds on the deviation of a function from its integral mean. The aim of this paper is to establish a new inequality using weight function which generalizes the inequalities of Dragomir, Wang and Cerone…
Quantum inequalities are lower bounds for local averages of quantum observables that have positive classical counterparts, such as the energy density or the Wick square. We establish such inequalities in general (possibly interacting)…
In this work, using the well-known mean-value theorem (Lagrange's theorem) we obtain an inequality for n-th order differential equations with retarded argument. If the retarded argument vanishes then the inequality turns to an inequality…
A quantum inequality for the quantized electromagnetic field is developed for observers in static curved spacetimes. The quantum inequality derived is a generalized expression given by a mode function expansion of the four-vector potential,…
In this paper, we establish new inequalities of Ostrowski type for functions whose derivatives in absolute value are m-convex. We also give some applications to special means of positive real numbers. Finally, we obtain some error estimates…
Our goal in this work is to present some mean value type theorems that are not studied in classic calculus and analysis courses. They are simple theorems yet with large applicability in mathematical analysis (for example, in the study of…
We use the definition of a fractional integral, recently proposed by Katugampola, to establish a generalization of the reverse Minkowski's inequality. We show two new theorems associated with this inequality, as well as state and show other…
We show a practical application of an well-known nonequilibrium relation, the Jarzynski equality, in quantum computation. Its implementation may open a way to solve combinatorial optimization problems, minimization of a real single-valued…
In this paper, we define a quantum analogue of the notion of empirical measure in the classical mechanics of $N$-particle systems. We establish an equation governing the evolution of our quantum analogue of the $N$-particle empirical…
This paper proposes a quantum circuit for computing the mean value from a given set of numbers or function evaluations. Suppose a Quantum Random Access Memory is given as a black-box function, which allows us to store and read the values of…
In this note, we establish new an inequality of Ostrowski-type for double integrals involving functions of two independent variables by using fairly elementary analysis.
The equipartition theorem is crucial in classical statistical physics, and recent studies have revealed its quantum counterpart for specific systems. This raises the question: does a quantum counterpart of the equipartition theorem exist…
The present paper is devoted to possible generalizations of the classic Lagrange Mean Value Theorem. We consider a real-valued function of several variables that is only assumed to be continuous. The main concept is to replace the notion of…
We develop some of the basic theory for the obstacle problem on Riemannian Manifolds, and we use it to establish a mean value theorem. Our mean value theorem works for a very wide class of Riemannian manifolds and has no weights at all…
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…