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In this paper, the mixed-type linear and Euler-Lagrange-Rassias functional equations introduced by J. M. Rassias is generalized to the following  n-dimensional functional equation:  f(Ã¢ÂˆÂ‘i=1nxi)+(nÃ¢ÂˆÂ’2)Ã¢ÂˆÂ‘i=1nf(xi)=Ã¢ÂˆÂ‘1Ã¢Â‰Â¤i<jÃ¢Â‰Â¤nf(xiÃ¢ÂˆÂ’xj) when n>2. We prove the general solutions and investigate its generalized Ulam-Gavruta-Rassias stability

On the Generalized Ulam-Gavruta-Rassias Stability of Mixed-Type Linear and Euler-Lagrange-Rassias Functional Equations