کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4673304 1346625 2007 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Decomposer and associative functional equations
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
چکیده انگلیسی

In the previous researches [2,3] b-integer and b-decimal parts of real numbers were introduced and studied by M.H. Hooshmand. The b-parts real functions have many interesting number theoretic explanations, analytic and algebraic properties, and satisfy the functional equation f (f(x) + y - f(y)) = f(x). These functions have led him to a more general topic in semigroups and groups (even in an arbitrary set with a binary operation [4] and the following functional equations have been introduced: Associative equations:f(xf(yz))=f(f(xy)z),f(xf(yz))=f(f(xy)z)=f(xyz)f(xf(yz))=f(f(xy)z),f(xf(yz))=f(f(xy)z)=f(xyz). Decomposer equations:f(f*(x)f(y))=f(y),f(f(x)f*(y))=f(x)f(f*(x)f(y))=f(y),f(f(x)f*(y))=f(x).Strong decomposer equations:f(f*(x)y)=f(y),f(xf*(y))=f(x)f(f*(x)y)=f(y),f(xf*(y))=f(x).Canceler equations:f(f(x)y)=f(xy),f(xf(y))=f(xy),f(xf(y)z)=f(xyz)f(f(x)y)=f(xy),f(xf(y))=f(xy),f(xf(y)z)=f(xyz), where f*(x) f(x) = f (x) f* (x) = x. In this paper we solve them and introduce the general solution of the decomposer and strong decomposer equations in the sets with a binary operation and semigroups respectively and also associative equations in arbitrary groups. Moreover we state some equivalent equations to them and study the relations between the above equations. Finally we prove that the associative equations and the system of strong decomposer and canceler equations do not have any nontrivial solutions in the simple groups.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Indagationes Mathematicae - Volume 18, Issue 4, 2007, Pages 539–554
نویسندگان
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