Open AccessTauberian conditions under which convergence follows from the weighted mean summability and its statistical extension for sequences of fuzzy number
Author(s) -
Zerrin Önder,
İbrahi̇m Çanak
Publication year - 2021
Publication title -
ukraïnsʹkij matematičnij žurnal
Language(s) - English
Resource type - Journals
ISSN - 1027-3190
DOI - 10.37863/umzh.v73i8.584
Subject(s) - mathematics , limit (mathematics) , sequence (biology) , abelian and tauberian theorems , converse , extension (predicate logic) , convergence (economics) , fuzzy logic , combinatorics , discrete mathematics , pure mathematics , mathematical analysis , genetics , geometry , computer science , economics , biology , programming language , economic growth , linguistics , philosophy
UDC 517.5Let be a sequence of nonnegative numbers such that andLet be a sequence of fuzzy numbers.The weighted mean of is defined byIt is known that the existence of the limit implies that of For the the existence of the limit - we require the boundedness of in addition to the existence of the limit But, in general, the converse of this implication is not true. In this paper, we obtain Tauberian conditions, under which the existence of the limit follows from that of or - These Tauberian conditions are satisfied if satisfies the two-sided condition of Hardy type relative to