Study of fixed point theorems, contractive and non contractive mapping

The accomplishments in the field of functional analysis in the last few decades are mainly the developments of new creative methods to use the fundamental tools of functional analysis, either in theory where they had not been applied before or in the construction of more powerful directions to handle functional analysis. Functional analysis embodies the abstract approach in analysis; it studies the functions rather than an individual function. It gives many fundamental notions relevant for the description, analysis, numerical approximation, medicine, ecology, agro- industries and computer simulation processes. It also discovers solutions to problems occurring in pure, applied and social sciences.