g-chordal curves

In this paper we introduce a notion of g-chordal curves which are a natural generalization of equichordal, equireciprocal and equipower curves. A Crofton-type integral formula and estimations of the area and the length of g-chordal curve are given. Moreover, a 1-parameter family of ovals with exactly four vertices in the class generated by the function g (x) = xm is constructed. A remark on the equichordal problem ends the paper.