Estimation of eigenvalues for the $\alpha$-Laplace operator on pseudo-slant submanifolds of generalized Sasakian space forms

In this study, we seek to establish new upper bounds for the mean curvature and constant sectional curvature of the first positive eigenvalue of the $\alpha$-Laplacian operator on Riemannian manifolds. More precisely, various methods are used to determine the first eigenvalue for the $\alpha$-Laplacian operator on the closed oriented pseudo-slant submanifolds in a generalized Sasakian space form. From our findings for the Laplacian, we extend many Reilly-like inequalities to the $\alpha$-Laplacian on pseudo slant submanifold in a unit sphere.