A functional equation motivated by some trigonometric identities

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• 作者：Włodzimierz Fechner^a ; ^{wlodzimierz.fechner@p.lodz.pl} ; Żywilla Fechner^b ; ^{zfechner@gmail.com}
• 关键词：Functional equation ; Trigonometric functions
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 May 2017
• 年：2017
• 卷：449
• 期：2
• 页码：1160-1171
• 全文大小：316 K
• 卷排序：449

文摘

We deal with the following functional equation:f(xy)+λf(x)f(y)=ϕ(x,y),f(xy)+λf(x)f(y)=ϕ(x,y), where λ is a complex number and f and ϕ are complex mappings defined on a semigroup. Moreover, we assume an addition formula of trigonometric type for ϕ. Our research is motivated by some earlier results related to a problem posed by S. Butler in 2003.