Parmeshwary Dayal Srivastava

Biography

Parmeshwary Dayal Srivastava is an Assistant Professor in the Department of Mathematics at IIT Kharagpur.

Research Interest

My work is mainly motivated by the development of the theory of sequence and function spaces in real or complex numbers and fuzzy numbers over the past few decades in one direction and Security weaknesses of protocols for digital signatures, smart-card authentication and access control in other direction . In the present day ,theory of sequence spaces is no more limited to the summability theory alone but has gone much beyond with the applications of functional analysis and structural theory of topological vector spaces. An attempt is made by us to study the theory of sequence spaces in regards to some of recent aspects like the scalar & vector valued sequences, Orlicz & Modulus functions , duality theory , statistical convergence , Spectrum of difference operators etc. The study of proper basis in a complete linear metric spaces is also made which unifies many known results by earlier workers such as Iyer ,Arsove ,Krisnamurthy and others. Recently, I have shown interest to introduce and study new sequence spaces using the various type of convergence such as statistical convergence, lacunary convergence etc. In this direction I have extended the concept of statistical convergence in a composite vector valued /scalar valued sequence spaces, double sequence spaces, -difference double sequence spaces etc. Lacunary convergent double sequence spaces and the operator dual of some generalized sequence spaces are also studied. I have studied some existing protocols for digital signatures, smart-card authentication and access control and Security weaknesses are identified in these protocols. Moreover, improvements are proposed to remove these security weaknesses.