Related papers: A Generalisation of an Ostrowski Inequality in Inn…
We introduce a product in all complex normed vector spaces, which generalizes the inner product of complex inner product spaces. Naturally the question occurs whether the Cauchy-Schwarz inequality is fulfilled. We provide a positive answer.…
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…
New reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces are pointed out. These results complement the recent ones obtained by the author in an earlier paper. Further, they are employed to establish new Gruss…
We introduce a affine geometric quantity and call it Orlicz mixed chord integral, which generalize the chord integrals to Orlicz space. Minkoswki and Brunn-Minkowski inequalities for the Orlicz mixed chord integrals are establish. These new…
In this paper we generalize the classical Nikol'skii inequality on the many popular classes pairs of rearrangement invariant (r.i.) spaces and construct some examples in order to show the exactness of our estimations.
We study a family of inequalities on pairs of measure spaces involving functions defined on product domains. Our main result establishes a Jensen-type inequality under a general product-measure framework, extending classical inequalities…
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 paper we parallelly build up the theories of normed linear spaces and of linear spaces with indefinite metric, called also Minkowski spaces for finite dimensions in the literature. In the first part of this paper we collect the…
In this paper, we establish Ostrowski's type inequalities for strongly-convex functions where c>0 by using some classical inequalities and elemantery analysis. We also give some results for product of two strongly-convex functions.
New reverses of the Schwarz inequality in inner product spaces that incorporate the classical Klamkin-McLenaghan result for the case of positive n-tuples are given. Applications for Lebesgue integrals are also provided.
In this note, we present two general classes of integral inequalities motivated by their applications to infinite dimensional systems. The inequalities possess general structures in terms of weight functions and lower quadratic bounds. Many…
Often, when we consider the time evolution of a system, we resort to approximation: Instead of calculating the exact orbit, we divide the time interval in question into uniform segments. Chernoff's results in this direction provide us with…
We generalize the classical Minkowski integral inequality to the form involving general Banach function norms.
In this paper, some new inequalities of Ostrowski type established for the class of m- and (alpha,m)-geometrically convex functions which are generalizations of geometric convex functions.
We prove in this article the generalizations on the exponential Orlicz spaces Markov's - Bernstein's inequalities for algebraic polynomials and rational functions.
In this paper, we obtained some new Ostrowski-Gruss type inequalities contains twice differentiable 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.
We study the Cauchy--Schwarz and some related inequalities in a semi-inner product module over a $C^*$-algebra $\A$. The key idea is to consider a semi-inner product $\A$-module as a semi-inner product $\A$-module with respect to another…
Generalized product formulas and index transforms, involving products of Whittaker's functions of different indices are established and investigated. The corresponding inversion formulas are found. Particular cases cover index transforms…
In this paper, new versions of Chebyshev's, Minkowski's and Holder's type inequalities are studied by using a monotone measure-base universal integral on an arbitrary measurable space. This paper generalizes some previous results obtained…