{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:53:22Z","timestamp":1777704802712,"version":"3.51.4"},"reference-count":41,"publisher":"SAGE Publications","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2021,6,21]]},"abstract":"<jats:p>Tauberian theorem serves the purpose to recuperate Pringsheim\u2019s convergence of a double sequence from its (C, 1, 1) summability under some additional conditions known as Tauberian conditions. In this article, we intend to introduce some Tauberian theorems for fuzzy number sequences by using the de la Vall\u00e9e Poussin mean and double difference operator of order r\u00a0. We prove that a bounded double sequence of fuzzy number which is \u0394 u r - convergent is ( C , 1 , 1 ) \u0394 u r - summable to the same fuzzy number L\u00a0. We make an effort to develop some new slowly oscillating and Hardy-type Tauberian conditions in certain senses employing de la Vall\u00e9e Poussin mean. We establish a connection between the \u0394 u r - Hardy type and \u0394 u r - slowly oscillating Tauberian condition. Finally by using these new slowly oscillating and Hardy-type Tauberian conditions, we explore some relations between ( C , 1 , 1 ) \u0394 u r - summable and \u0394 u r - convergent double fuzzy number sequences.<\/jats:p>","DOI":"10.3233\/jifs-202921","type":"journal-article","created":{"date-parts":[[2021,3,16]],"date-time":"2021-03-16T13:44:45Z","timestamp":1615902285000},"page":"11799-11808","source":"Crossref","is-referenced-by-count":1,"title":["Applications of Tauberian theorems for double sequences of fuzzy numbers via De La Vall\u00e9e Poussin mean"],"prefix":"10.1177","volume":"40","author":[{"given":"Anu","family":"Choudhary","sequence":"first","affiliation":[{"name":"School of Mathematics, Shri Mata Vaishno Devi University, Katra, J & K, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kuldip","family":"Raj","sequence":"additional","affiliation":[{"name":"School of Mathematics, Shri Mata Vaishno Devi University, Katra, J & K, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Mursaleen","sequence":"additional","affiliation":[{"name":"Al-Qaryah, Doharra, Aligarh, India"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-202921_ref1","doi-asserted-by":"crossref","unstructured":"Arendt W. , Batty C. , Hieber M. and Neubrander F. , Vector-valued Laplace transforms and Cauchy problems, Monogr Math 96 (2001), Birkh\u00e4user Verlag, Basel.","DOI":"10.1007\/978-3-0348-5075-9"},{"key":"10.3233\/JIFS-202921_ref2","first-page":"287","article-title":"On difference double sequence spaces of fractional order","volume":"58","author":"Baliarsingh","year":"2016","journal-title":"Indian J Math"},{"key":"10.3233\/JIFS-202921_ref3","first-page":"193","article-title":"On some double sequence spaces","volume":"21","author":"Ba\u015farir","year":"1999","journal-title":"J Indian Acad Math"},{"key":"10.3233\/JIFS-202921_ref4","doi-asserted-by":"crossref","unstructured":"Bede B. , Mathematics of fuzzy sets and fuzzy logic, 1st ed., Springer-Verlag, Berlin, 2013.","DOI":"10.1007\/978-3-642-35221-8_1"},{"key":"10.3233\/JIFS-202921_ref5","doi-asserted-by":"crossref","first-page":"695","DOI":"10.18514\/MMN.2015.1254","article-title":"Tauberian conditions under which \u03bb- statistical convergence follows from statistical summability (V, \u03bb)","volume":"16","author":"Braha","year":"2015","journal-title":"Miskolc Math Notes"},{"key":"10.3233\/JIFS-202921_ref6","unstructured":"Bromwich T. 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