Inter relationship between the notion of fixed point, Kutasth Vindu and Vedanta philosophy

Abstract

Fixed point theory is a rich, interesting and exciting branch of mathematics. It is relatively young but fully developed area of research. Study of the existence of fixed points falls within several domains such as functional analysis, operator theory, general topology. Fixed points and fixed point theorems have always been a major theoretical tool in fields as widely apart as topology, mathematical economics, game theory, approximation theory and initial and boundary value problems in ordinary and partial differential equations. Moreover, recently, the usefulness of this concept for applications increased enormously by the development of accurate and efficient techniques for computing fixed points, making fixed point methods a major tool in the arsenal of mathematics. The theory of fixed points is concerned with the conditions which guarantee that a map T : X g X of a topological space X into itself. admits one or more fixed points that is, points x in X for which x = Tx. The Sanskrit word kutastha means “that which remains unchanged”. Vedanta, the most prominent school of Hinduism, is a philosophical system that is concerned with questions such as ‘Who am I?’, ‘What is this Universe?’ ‘How am I related to the Universe?’ In this paper we discuss fixed point notion, kutastha vindu and Vedanta Philosophy and also to find their interrelationship used in Hindu mythological books.