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چکیده
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Our aim of this paper is to study a family of functional equation in vector and Banach spaces with difference operators, where this family of functional equation is a general mixed additive-quadratic-cubic-quartic functional equations. We show that every function satisfies the our functional equation is a monomial function with a certain degree. Furthermore, we deal with the generalized Hyers-Ulam stability of this family of functional equations in Banach space
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