In this article, we introduce the multi-additive-quartic and the multimixed additive-quartic mappings. We also describe and characterize the structure of such mappings. In other words, we unify the system of functional equations defining a multi-additive-quartic or a multimixed additive-quartic mapping to a single equation. We also show that under what conditions, a multimixed additive-quartic mapping can be multiadditive, multiquartic, and multi-additive-quartic. Moreover, by using a fixed point technique, we prove the Hyers-Ulam stability of multimixed additive-quartic functional equations thus generalizing some known results.

Let p(z) be a polynomial of degree n and for any complex number α, D α p(z) = np(z)+(α−z)p ′ (z) denote the polar derivative of the polynomial p(z) with respect to α. In this paper, we obtain new results concerning maximum modulus of the polar derivative of a polynomial with restricted zeros. Our result generalize certain well-known polynomial inequalities.

No abstract