http://starc.stthomas.ac.in:8080/xmlui/xmlui/handle/123456789/151 2026-04-27T00:14:04Z http://starc.stthomas.ac.in:8080/xmlui/xmlui/handle/123456789/159 On the relation of generalized Valiron summability to Ces'aro summability Krishnan, VK A family (Va ~) of summability methods, called generalized Valiron summability, is defined. The well-known summability methods (Ba, 7), (Er (Ta), (SI~) and (Va) are members of this fami!y. In w some properties of the (Ba,~,) and (V~) transforms are established. Following Satz II of Faulhaber (1956) it is proved that the members of the (V~) family are all equivalent for sequences of finite order. This paper is a good illustration of the use of generalized Boral summability. The following theorem is established: Theorem. /f s n (n ~ 0) is a real sequence satisfying lira lim inf min (s, ~ sin" ~ e->0+ ~-~o ,.~<.~,,+ex/., \--m-P-./> o (p ~> 0), and if s n --* s (V~) then s, ---> s (C, 2p). 1980-05-03T00:00:00Z http://starc.stthomas.ac.in:8080/xmlui/xmlui/handle/123456789/157 Gap Tauberian Theorem For Logarithmic Summability (L) Krishnan, VK 1977-12-22T00:00:00Z http://starc.stthomas.ac.in:8080/xmlui/xmlui/handle/123456789/152 Gap Tauberian theorem for generalized Abel summability Krishnan, VK 1974-11-25T00:00:00Z