2000 Mathematics Subject Classification: 26D10, 26D15.Here are presented Ostrowski type inequalities over spherical shells. These regard sharp or close to sharp estimates to the difference of the average of a multivariate function from its value at a point.
Some Ostrowski’s type inequalities for the Riemann-Stieltjes integral of continuous complex valued integrands defined on the complex unit circle and various subclasses of integrators of bounded variation are given. Natural applications for functions of unitary operators in Hilbert spaces are provided as well.
We consider a multifunction , where T, X and E are separable metric spaces, with E complete. Assuming that F is jointly measurable in the product and a.e. lower semicontinuous in the second variable, we establish the existence of a selection for F which is measurable with respect to the first variable and a.e. continuous with respect to the second one. Our result is in the spirit of [11], where multifunctions of only one variable are considered.
In this article, we aim to prove the characterization of differentiation by means of partial differentiation for vector-valued functions on n-dimensional real normed linear spaces (refer to [15] and [16]).
In this article, we define and develop partial differentiation of vector-valued functions on n-dimensional real normed linear spaces (refer to [19] and [20]).