On generalized Cesàro stable functions

Abstract

The notion of Cesàro stable function is generalized by introducing Cesàro mean of type $(b-1;c)$ which give rise to a new concept of generalized Cesàro stable function. As an application of generalized Cesàro stable functions we also prove for a convex function of order $\lambda \in [1/2,1)$, its Cesàro mean of type $(b-1;c)$ is close-to-convex of order $\lambda$. Further two conjectures are also posed in the direction of generalized Cesàro stable function. Some particular cases of these conjectures are also discussed.

19 pages