Decomposer and associative functional equations |
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| Authors: | MH Hooshmand Hailiza K Haili |
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| Institution: | aSchool of Mathematical Sciences, University Science of Malaysia, Penang, Malaysia |
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| Abstract: | 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) | . Decomposer equations:f(f*(x)f(y))=f(y),f(f(x)f*(y))=f(x) f(f*(x)y)=f(y),f(xf*(y))=f(x) f(f(x)y)=f(xy),f(xf(y))=f(xy),f(xf(y)z)=f(xyz)
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| Keywords: | Functional equation Binary operation Conjugations of functions b-integer and b-decimal parts of real numbers b-parts real functions Decomposer equation Associative equation Canceler equation General solution |
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