Lower bounds for a certain class of error functions

Lower bounds for a certain class of error functions

On error bounds for lower semicontinuous functions

We give some sufficient conditions for proper lower semicontinuous functions on metric spaces to have error bounds (with exponents). For a proper convex function f on a normed space X the existence of a local error bound implies that of a global error bound. If in addition X is a Banach space, then error bounds can be characterized by the subdifferential of f . In a reflexive Banach space X, we...

Certain Inequalities for a General Class of Analytic and Bi-univalent Functions

In this work, the subclass of the function class S of analytic and bi-univalent functions is defined and studied in the open unit disc. Estimates for initial coefficients of Taylor- Maclaurin series of bi-univalent functions belonging these class are obtained. By choosing the special values for parameters and functions it is shown that the class reduces to several earlier known classes of analy...

Uniform Error Bounds for Reconstruct Functions from Weighted Bernstein Class

Errors appear when the Shannon sampling series is applied to reconstruct a signal in practice. This is because the sampled values may not be exact, or the sampling series may have to be truncated. In this paper, we study errors in truncated sampling series with localized sampling for band-limited functions from weighted Bernstein class. And we apply these results to some practical examples.

A certain convolution approach for subclasses of univalent harmonic functions

In the present paper we study convolution properties for subclasses of univalent harmonic functions in the open unit disc and obtain some basic properties such as coefficient characterization and extreme points.