• Dr. Amar Nath Kumar
• Dr. Krishnandan Prasad

Ko ̈the and Toeplitz, (1) have carried out works on sequence spaces some of which were later on developed by Allen, (1) and Dienes,P., (1). an account of all these can be found out in [Cooke, (1),chapter 10]. In this direction of study efforts were made to establish some of the results. we experienced that in sequence spaces αβ-limit implies c-limit of the same sequence in a sequence space. But there we did not get an authentic signal for a c-limit to be αβ-limit under αβ-convergence. In order to examine the problems of existence and the position of these limits Dienes,(1) introduced the notion of regular sequence spaces. Our sincere efforts in this paper is to study sequence spaces in detail to observe that under what circumstances some of the sequence spaces fall to be regular.Ko ̈the and Toeplitz, (1) have carried out works on sequence spaces some of which were later on developed by Allen, (1) and Dienes,P., (1). an account of all these can be found out in [Cooke, (1),chapter 10]. In this direction of study efforts were made to establish some of the results. we experienced that in sequence spaces αβ-limit implies c-limit of the same sequence in a sequence space. But there we did not get an authentic signal for a c-limit to be αβ-limit under αβ-convergence. In order to examine the problems of existence and the position of these limits Dienes,(1) introduced the notion of regular sequence spaces. Our sincere efforts in this paper is to study sequence spaces in detail to observe that under what circumstances some of the sequence spaces fall to be regular.

Linear Space, Sequence Space, Dual Sequence Space, Perfect Sequence Space, Normal Sequence Space, Regular Sequence Space, Co-Ordinate Limit,Projective limit.

"A NOTE ON REGULAR SEQUENCE SPACE", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.7, Issue 2, page no.1122-1128, February-2020, Available :http://www.jetir.org/papers/JETIR2002371.pdf

"A NOTE ON REGULAR SEQUENCE SPACE", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.7, Issue 2, page no. pp1122-1128, February-2020, Available at : http://www.jetir.org/papers/JETIR2002371.pdf