This paper studies some properties of F-biharmonic maps between Riemannian manifolds. By considering the first variation formula of the F-bienergy functional, F-biharmonicity of conformal maps are investigated. Moreover, the second variation formula for F-biharmonic maps is obtained. As an application, instability and nonexistence theorems for F-biharmonic maps are given.

The dynamical behavior of a map on the unit interval has been the subject of much contemporary research. In this paper, we will consider the relation between the continuity of the map cof and cof for some positive integer k, where f is a continuous map from the unit interval to itself, and ?f is a function which takes any element of the unit interval to the set of all subsequential limits o...