Research Projects

The application of q-theory was initially given by Jackson who identified the q-analogue of derivative and integral operators. Since then q-theory or q-analog attracted the interests of mathematical community resulting into several applications of q-calculus in the area of combinatorics, special functions, algebras, approximation theory, integro-differential equations, fractional calculus, etc. However, the applications of q-calculus have been realized very recently in the field of summability and sequence spaces. In particular, in the field of difference sequence spaces, couple of papers could be traced in the literature that deals with the application of q-theory. In this project, we wish to study the domain of q-difference operators in Hahn sequence spaces and study several interesting properties of the resulting sequence spaces. We further wish to construct some new generalized q-difference operators and study the associated sequence spaces.