  Inspired by a recent work of Mesnager, we present several new infinite
families of quadratic ternary bent, near-bent and 2-plateaued functions from
some known quadratic ternary bent functions. Meanwhile, the distribution of the
Walsh spectrum of two class of 2-plateaued functions obtained in this paper is
completely determined. Additionally, we construct the first class of $p$-ary
bent functions of algebraic degree $p$ over the fields of an arbitrary odd
characteristic. The proposed class contains non-quadratic $p$-ary bent
functions that are affinely inequivalent to known monomial and binomial ones.
