{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:42:30Z","timestamp":1777704150565,"version":"3.51.4"},"reference-count":34,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2018,7,9]],"date-time":"2018-07-09T00:00:00Z","timestamp":1531094400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2018,8,26]]},"abstract":"<jats:p>\n                    In this paper we introduce and study some difference double sequence spaces of fuzzy numbers by using Hausdorff metric associated with sequence of Orlicz functions. We make an effort to study some algebraic, topological properties and inclusion relations between these sequence spaces. We show that the new formed sequence spaces are complete with respect to the metric\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:msup>\n                          <mml:mi>D<\/mml:mi>\n                          <mml:mrow>\n                            <mml:mi mathvariant=\"script\">M<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>\u0394<\/mml:mi>\n                              <mml:mi mathvariant=\"script\">m<\/mml:mi>\n                            <\/mml:msup>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi mathvariant=\"script\">p<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi mathvariant=\"script\">u<\/mml:mi>\n                          <\/mml:mrow>\n                        <\/mml:msup>\n                        <mml:mo>(<\/mml:mo>\n                        <mml:mi>x<\/mml:mi>\n                        <mml:mo>,<\/mml:mo>\n                        <mml:mi>y<\/mml:mi>\n                        <mml:mo>)<\/mml:mo>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    . Finally, we establish some relation between\n                    <jats:italic>\u0394<\/jats:italic>\n                    <jats:sup>\n                      <jats:italic>r<\/jats:italic>\n                    <\/jats:sup>\n                    -statistically convergent and\n                    <jats:italic>\u0394<\/jats:italic>\n                    <jats:sup>\n                      <jats:italic>r<\/jats:italic>\n                    <\/jats:sup>\n                    -statistically (\n                    <jats:italic>C<\/jats:italic>\n                    , 1, 1) summable double sequences of fuzzy numbers under the slowly oscillating and statistically slowly oscillating conditions in certain sense, respectively.\n                  <\/jats:p>","DOI":"10.3233\/jifs-18195","type":"journal-article","created":{"date-parts":[[2018,7,10]],"date-time":"2018-07-10T14:42:29Z","timestamp":1531233749000},"page":"2513-2524","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Applications of Tauberian theorem in Orlicz spaces of double difference sequences of fuzzy numbers"],"prefix":"10.1177","volume":"35","author":[{"given":"Kuldip","family":"Raj","sequence":"first","affiliation":[{"name":"School of Mathematics, Shri Mata Vaishno Devi University, Katra, J &amp; K, India"}]},{"given":"Charu","family":"Sharma","sequence":"additional","affiliation":[{"name":"School of Mathematics, Shri Mata Vaishno Devi University, Katra, J &amp; K, India"}]},{"given":"Anu","family":"Choudhary","sequence":"additional","affiliation":[{"name":"School of Mathematics, Shri Mata Vaishno Devi University, Katra, J &amp; K, India"}]}],"member":"179","published-online":{"date-parts":[[2018,7,9]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-35221-8"},{"key":"e_1_3_2_3_2","unstructured":"BromwichT.J. An introduction to the theory of infinite series Macmillan and Co.Ltd New York 1965."},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-151999"},{"key":"e_1_3_2_5_2","first-page":"87","article-title":"Holder summability method of fuzzy numbers and a Tauberian theorem","volume":"11","author":"\u00c7anak I.","year":"2014","unstructured":"\u00c7anakI., Holder summability method of fuzzy numbers and a Tauberian theorem, Iranian Journal of Fuzzy Systems 11 (2014), 87\u201393.","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"e_1_3_2_6_2","first-page":"61","article-title":"A Tauberian theorem for (1, 1) summable double sequences of fuzzy numbers","volume":"14","author":"\u00c7anak I.","year":"2017","unstructured":"\u00c7anakI. Totur\u00dc. and \u00d6nderZ., A Tauberian theorem for (1, 1) summable double sequences of fuzzy numbers, Iranian Journal of Fuzzy Systems 14 (2017), 61\u201375.","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(90)90197-E"},{"key":"e_1_3_2_8_2","first-page":"377","article-title":"On generalized difference sequence spaces","volume":"21","author":"Et M.","year":"1995","unstructured":"EtM. and ColakR., On generalized difference sequence spaces, Soochow Journal of Mathematics 21 (1995), 377\u2013386.","journal-title":"Soochow Journal of Mathematics"},{"key":"e_1_3_2_9_2","first-page":"86","article-title":"On the convergence of certain multiple series","volume":"19","author":"Hardy G.H.","year":"1917","unstructured":"HardyG.H., On the convergence of certain multiple series, Proceedings of the London Mathematical Society 19 (1917), 86\u201395.","journal-title":"Proceedings of the London Mathematical Society"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1981-027-5"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10474-015-0550-5"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10998-011-8205-y"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.4064\/sm-45-2-119-146"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02771656"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/26.3.288"},{"key":"e_1_3_2_16_2","volume-title":"Orlicz spaces and interpolation","author":"Maligranda L.","year":"1989","unstructured":"MaligrandaL. 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