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Summary: In this paper, we introduce the following $$(a, b, c)$$-mixed type functional equation of the form $\begin{split} g(ax_1+bx_2+cx_3)-g(-ax_1+bx_2+cx_3) +g(ax_1-bx_2+cx_3)-g(ax_1+bx_2-cx_3) +\\ 2a^2[g(x_1) +g(-x_1)] + 2b^2[g(x_2) +g(-x_2)] + 2c^2[g(x_3) +g(-x_3)] +a[g(x_1)-g(-x_1)] +\\ b[g(x_2)-g(-x_2)] +c[g(x_3)-g(-x_3)] = 4g(ax_1+cx_3) + 2g(-bx_2) + 2g(bx_2) \end{split}$ where $$a$$, $$b$$, $$c$$ are positive integers with $$a >1$$, and investigate the solution and the Hyers-Ulam stability of the above functional equation in Banach spaces by using two different methods.