Fixed Point Developed by Space Topology
ISSN : 2394-3580 Swadeshi Research Foundation Vol. – 6, No. - 10 August 2019 A Monthly Journal of Multidisciplinary International Peer Refereed, Review, Indexing & Impact Factor - 4.2 Research Journal Fixed point developed by space Topology Dr. V.H. Badshah Professor and Head, School of Studies in Mathematics, Vikram University, Ujjain Santoshi Alawa Research Scholar The theory of fixed point is one of the most The same definition of recursive function powerful tool of modern Mathematics. It is a rich, can be given, in by applying these results are not interesting and exciting branch of Mathematics. equivalent theorems; the Knaster–Tarski theorem Theorems Concerning the existence and properties is a much stronger result than what is used in de of Fixed points are known as fixed point theorem. notational semantics.[11] However, in light of It is a beautiful mixture of Analysis, Topology and the their intuitive meaning is the same: a Geometry. Fixed point theorems are applied in recursive function can be described as the least various fields such as Engineering, Physics, fixed point of a certain functional, mapping Chemistry, Economics, Game theory, Biology, functions to functions. Medical science, Classical analysis, Functional The above technique of iterating a function to analysis, Functional analysis, Integral equations, find a fixed point can also be used in the states Differential equations, Partial differential that any continuous strictly increasing function equations, Eigen Value problems, Boundary Value from to ordinals has one (and indeed many) fixed problems, analysis, Operator theory, Theory of points. Every on a posset has many fixed points; Non-Linear Oscillations, General and Algebraic these are the "closed elements" with respect to Topology etc.
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