Study Of Fixed Point Theorems On Metric And Certain Topological Spaces

Abstract

The term metric fixed point theory refers to those fixed points theoretic results in newlinewhich geometric conditions on the underlying spaces and/or mapping plays a crucial newlinerole. For the past many years fixed point theory has been flourishing area for many newlinemathematician. Although a substantial number of definitive results have now been newlinediscovered, a few question lying at the heart of the theory remain open and there are newlinemany unanswered question regarding the limits to which the theory may be extended. newlineSome of these questions are merely tantalizing while others suggest substantial new newlineavenues of research. newlineFixed point theorems for single-valued and multivalued mapping have been studied newlineextensively and applied to diverse problems during the last few decades. In 1922, the newlinePolish mathematician, Banach [13], proved a theorem which ensures, under appropriate conditions, the existence and uniqueness of a fixed point. His result is called newlineBanach s fixed point theorem or the Banach contraction principle. This theorem provides a technique for solving a variety of applied problems in mathematical science and newlineengineering. Many authors have extended, generalized and improved Banach s fixed newlinepoint theorem in different ways. newlineIn mathematics, a fixed point (also know as an invariant point) of a function is a point newlinethat is mapped to itself by function. Let f be a function which maps a set L into newlineitself; i.e f : L and#8594; L. A fixed point of the mapping f is an element w and#8712; L such that newlinef(w) = w. newlineA lot of work has been done on fixed point with different type of mapping and newlinespaces. An attempt has been put to discuss the problems entitled STUDY OF newlineFIXED POINT THEOREMS ON METRIC AND CERTAIN TOPOLOGICAL SPACES over the period of my research work. newline