Variational Inequalities for the Fractional Laplacian

Stability of variational eigenvalues for the fractional p–Laplacian

By virtue of Γ−convergence arguments, we investigate the stability of variational eigenvalues associated with a given topological index for the fractional p−Laplacian operator, in the singular limit as the nonlocal operator converges to the p−Laplacian. We also obtain the convergence of the corresponding normalized eigenfunctions in a suitable fractional norm.

Two generalized Lyapunov-type inequalities for a fractional p-Laplacian equation with fractional boundary conditions

In this paper, we investigate the existence of positive solutions for the boundary value problem of nonlinear fractional differential equation with mixed fractional derivatives and p-Laplacian operator. Then we establish two smart generalizations of Lyapunov-type inequalities. Some applications are given to demonstrate the effectiveness of the new results.

Strong convergence for variational inequalities and equilibrium problems and representations

We introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition for ...

More inequalities for Laplacian indices by way of majorization

The n-tuple of Laplacian characteristic values of a graph is majorized by the conjugate sequence of its degrees. Using that result we find a collection of general inequalities for a number of Laplacian indices expressed in terms of the conjugate degrees, and then with a maximality argument, we find tight general bounds expressed in terms of the size of the vertex set n and the average degree dG...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points