کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4622527 1339500 2007 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
“Pexiderized” homogeneity almost everywhere
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
“Pexiderized” homogeneity almost everywhere
چکیده انگلیسی

In the paper we examine Pexiderized ϕ-homogeneity equation almost everywhere. Assume that G and H   are groups with zero, (X,G)(X,G) and (Y,H)(Y,H) are a G- and an H  -space, respectively. We prove, under some assumption on (Y,H)(Y,H), that if functions ϕ:G→H and F1,F2:X→Y satisfy Pexiderized ϕ-homogeneity equationF1(αx)=ϕ(α)F2(x)F1(αx)=ϕ(α)F2(x) almost everywhere in G×XG×X then either ϕ=0ϕ=0 almost everywhere in G   or F2=θF2=θ almost everywhere in X   or there exists a homomorphism ϕ˜:G→H such that ϕ=aϕ˜ almost everywhere in G   and there exists a function F¯:X→Y such thatF¯(αx)=ϕ˜(α)F¯(x)for α∈G∖{0},x∈X, andF1=aF¯almost everywhere in X,F2=F¯almost everywhere in X, where a∈H∗a∈H∗ is a constant. From this result we derive solution of the classical Pexider equation almost everywhere.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 325, Issue 1, 1 January 2007, Pages 675–684
نویسندگان
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