STUDIES ON CERTAIN GEOMETRIC SEQUENCE SPACES

The study of sequence spaces occupies a very prominent position in Functional analysis, which has a vast range of applications in different branches of mathematics such as the structural theory of topological vector spaces, Schauder basis theory, ergodic theory, law of large numbers, summability theory and the theory of functions. The most important functions to which the problems of mathematical analysis, geometry, mechanics and physics lead are all analytic. This is the reason why analytic functions play such a vital role in mathematics. Due to its vast applications, the study of different subclasses of analytic functions with suitable topologies defined on it, has been vastly enriched in different directions.Geometric calculus is one type of non-Newtonian calculus based on geometric arithmetic generated by the function exp and it can be used as a tool for problems of exponential in nature. The main objective of the present work is to introduce the geometric sequence spaces based on different operator in geometric arithmetic.