泛函方程在广义模糊赋范空间中的稳定性.doc

-H“‰??a?? ?? M5`2 √  x-(2: d?¤J  a???5Aa·?·§32?  D‰?m￥ -?56, ′ 3 “· e, 3-H“‰??????” ”a?” ”? ?m?á? 1??ó?¤ ¤J. ??￥?52ü? ?·1|?2uL? ??¤ J. é ? ??ó?‰?-? z ?ú8N, t?3?￥?2( ·a52. (2 {?(Jò d ?ú.  ??\?:  F?:  -H“‰??a?? ??|^? √  ?  5Aa·?·§32?  D‰?m￥  -?56X  3-H“‰????a ?? ?m, 3 “· e ¤ ??” ”a?” ”? ??. ?? ??¤J8- H“‰??¤k, ?? ??SN? ±ù|ü ??uL.  )-H“ ‰??u ·!|^? ?? 5?, ó?? 3?·kü€x ?? E ?úf? , #N?? ú/ . ? -H“‰??, ?±?^K?ù| E??? ·??, ?±úmuL?? ü?ü?SN.  ??\?: “\?:  F?: F?: -H“‰??a?? á ?  ??  1965cZadehDgú\  8  Vg[1]. 3?a?  8n?  uD￥, ? ìuy ;8ü?￥ [. ˉ￠t, 3·C 40cp, n??2¤·?? 9€{K, 3‰?úó§? +·￥ 2·A^. ~X: ·???, ??5??X ú, ??5?f, úOCX. ó? ?àVg3tf?n?￥·?k-?A^. ,?·?, ??;. ˉK′-?5ˉK. ·?·§ -?5ˉK g Ulam 3 1940 cJ? u+ó -?5ˉK, 1941 c, D. H. Hyers )? Banach ?mt? \N -?5ˉK. 3 e5 A?cp, N?ê?[é???ó ·?·§ -? 5?1 Xú ??, ~XμCauchy·§, Jensen·§, ·ê·§, g·?·§, ng ·?·§±9·ü ·?·§ . 1978 c, Th. M. Rassias )? ?5N 3 Banach ?m￥ -?5ˉK; 1992c, Gzerwik )? g?\·?·§3D‰?m￥ -? 5; 1999 c Y. Lee ú K. Jun ?? 2? Jensen·§ -?5; 2002c, K.-W.JunúH.- M.Kim)? ng·?·§ -?5. ù -?5 ¤J3‘???, 7Kê?ú°? ê? +·￥tk2· A^. ? ?·üù. 31?ù￥, ·?|^??:·{??? CqCauchy-Jensen·?  N(f(  x + y 2  ) + f(  x ? y 2  ) ? f(x), t) ≥ N (?(x, y), t) 32? D‰?m￥ -?5ˉK. |^? {???Cq g?\.·?  N(f(x + 2y) + f(2x ? y) ? f(x + y) ? f(x ? y) ? 2f(x), t) ≥ N (?(x, y), t)  32?  D‰?m￥ -?5ˉK.  31 ù￥, ·??? ??? Cqngog·ü.·? N(f(x + 2y) + f(x ? 2y) ? f(x + y) ? f(x ? y) ? 2f(2x) + 2f(x), t) ≥ N (?(x, y), t)  32?  D‰?m￥ -?5ˉK.  …c:  Hyers-Ulam -?5; Cq·?; 2?  D‰?m; Cauchy-Jensen·?;  g ·?; ng·?; og·?. i -H“‰??a??  ??  Abstract The notion of fuzzy sets was ?rst introduced by Zadeh in 1965 ([1]). Among various developments of the theory of fuzzy sets, progressive development has been made to ?nd the fuzzy analogues of the classical set theory. In fact, the fuzzy theory has become an area of active research for the last 40 years. It has a wide range of applications in the ?eld of science an