Abstract
This paper aims to establish new upper bounds for the first positive eigenvalue of the Phi-Laplacian operator on Riemannian manifolds in terms of mean curvature and constant sectional curvature. The first eigenvalue for the Phi-Laplacian operator on dosed oriented m-dimensional semislant submanifolds in a Sasakian space form (M) over tilde (2k+1) (epsilon) is estimated in various ways. Several Reilly-like inequalities are generalized from our findings for Laplacian to the Phi-Laplacian on semislant submanifolds in a sphere S2n+1 with epsilon = 1 and Phi = 2.