Daniela Inoan

Generalized Golden Ratios defined by means

Abstract Golden Ratio is defined by a proportion corresponding to the geometric mean. We introduce a generalized Golden Ratio as a fixed point of an operator defined by an arbitrary mean satisfying certain conditions. An algorithm for the evaluation of the generalized Golden Ratio is obtained using Banach’s fixed point theorem. As applications we show that some problems in shape optimization correspond to some aesthetic standards introduced in the paper.

AN EXISTENCE RESULT FOR A VARIATIONAL-LIKE INEQUALITY

In this paper we establish an existence result for a class of generalised variational-like inequalities, when the functions used in their definition are of type ql and satisfy some general continuity assumptions. We use a Brezis-Nirenberg-Stampacchia type result. DOI: 10.1017/S0004972714000380

A recursive algorithm for Bernstein operators of second kind

The Bernstein operators of second kind were introduced by Paolo Soardi in 1990, in terms of a random walk on a certain hypergroup. They have the same relation with Chebyshev polynomials of second kind as the classical Bernstein operators have with Chebyshev polynomials of first kind. In this paper we describe a de Casteljau type algorithm for these operators.