Algebras of general convexity and general concavity, nonlinear programming, physics, and inequalities

Abstract

In this paper we introduced the fundamental elements of new algebras of general convexity and general concavity. This paper presents essential elements of a new general convex (concave) functional analysis. Applications in linear and nonlinear functional analysis, linear and nonlinear programming, physics, and inequalities are considered. Adequate to fundamental fact that every set has three own sides (upper, lower and middle) we introduced and consider three relativistic physics (general convex, general concave and middle) and three physics in the classical sense. In this context we obtain relativistic Einstein's theory as a relativistic physics on the middle transversal linear spaces. 2000 Mathematics Subject Classification. Primary: 04A25, 54E15, 47H10, 05A15. Secondary: 54H25, 54E24.