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On the construction of some functional inequalities via ECGM algorithm

The development of optimization theory originated with economic requirements and problems, where optimal strategy was to be determined mathematically. At about the same time, approximation theory, which was already well developed, experienced a reinvigoration brought about by the advent of electronic computers. In this paper, what follows, we recall the functional analysis that constitutes the framework of our development of an extended conjugate gradient algorithm that does not involve any approximation in any of its steps. This is a computational enhancement over the conventional conjugate gradient method which is dependent on some approximation theory. We use this improved algorithm for the construction of some functional inequalities.