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よってjcnj2 = n より、cn がに正になる慣用を使うとcn = p n と決めること ができる。よって式(33) は ajni = p njn¡1i (35) と表される。同様にして ayjni = p n1jn1i (36) が導かれる。式(36) のn をn1 に置き換えて式変形すると jni = ay p n jn¡1i = ¢¢¢ = (ay)n p n!. PÖì â â ò Ä †ê ?ËþoûÿŸlÿ¿ß»«À¯qû· U \ Þ6 TµÎ ý a*éÇ Æ†ÞÉaLõ ‹jûžÏ•h*Å¡ª ƒ/_­¸ÊëÕ ö bV ØîÇ_ðø¤ö‘iüGm ‘Tª‘êe ¾w«Jl‹ðx« p/èYÃã³^—³I=Qzÿ Ÿ „=dµí³HÊéL˜Ù> ¿ lÈ0Ž Ì_`?¥q6Ÿ§ý¥™ÙV©(^6¨Í‰3½ï„?¾s†sÝòY*¢f “žå³`Í„3 òD. 6 On some mixed integral inequalities As up(t) • z(t) from (311), we obtain up(t) • z(fi)exp µZ t fi n1A(¾)d¾ Z t fi n2B(s)exp µZ t s n1A(¾)d¾ ds (312) Using z(fi) = c in (312), we get the desired inequality (38) and hence the proof Remark 2 Note that when p = q = 1 the Theorem 32 reduces to the inequality established by BG Pachpatte in (12 page no40).

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