Related papers: The Generalized Wielandt Inequality in Inner Produ…
New results related to the Boas-Bellman generalisation of Bessel's inequality in inner product spaces are given.
Some new reverses for the generalised triangle inequality in inner product spaces and applications are given. Applications in connection to the Schwarz inequality are provided as well.
A new refinement of the triangle inequality is presented in normed linear spaces. Moreover, a simple characterization of inner product spaces is obtained by using the skew-angular distance.
We suggest a concept of generalized `angles' in arbitrary real normed vector spaces. We give for each real number a definition of an `angle' by means of the shape of the unit ball. They all yield the well known Euclidean angle in the…
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.…
Some reverses for the generalised triangle inequality in complex inner product spaces that improve the classical Diaz-Metcalf results and applications are given.
A generalisation of inner product spaces of an inequality due to Ostrowski and applications for sequences and integrals are given.
In this article, we discuss the equality of two inner products on a vector space. Particularly, we look at some geometric properties that are given to a vector space by an inner product namely, length and angle, and we ask under what…
Some sharp quadratic reverses for the generalised triangle inequality in inner product spaces and applications are given.
New results related to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.
Some new reverses of the Cauchy-Schwarz inequality in inner product spaces are presented in this paper.The results obtained here complement the recent work of the references.
Some new Gruss type inequalities in inner product spaces and applications for integrals are given.
The purpose of this survey is to give a comprehensive introduction to some classes of classical and recent analytic inequalities in Inner Product Spaces.
Some related results to Pecaric's inequality in inner product spaces that generalises Bombieri's inequality, are given.
In this article, we prove an inner product inequality for Hilbert space operators. This inequality, then, is utilized to present a general numerical radius inequality using convex functions. Applications of the new results include obtaining…
We present a general refinement of the Cauchy-Schwarz inequality over complete inner product spaces and show that it can be of interest for some statistical applications. This generalizes and simplifies previous results on the same subject.
Some inequalities in 2-inner product spaces generalizing Bessel's result that are similar to the Boas-Bellman inequality from inner product spaces, are given. Applications for determinantal integral inequalities are also provided.
We consider a generalized angle in complex normed vector spaces. Its definition corresponds to the definition of the well known Euclidean angle in real inner product spaces. Not surprisingly it yields complex values as `angles'. This…
In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation…
A generalisation of the Cassels and Greub-Reinboldt inequalities in complex or real inner product spaces and applications for isotonic linear functionals, integrals and sequences are provided.