An a posteriori error estimator based on shifts for positive Hermitian eigenvalue problems

This work deals with an a posteriori error estimator for Hermitian positive eigenvalue problems. The proposed estimator is based on the residual and the definition of suitable shifts in the matrix spectrum. The mathematical properties (certification and sharpness) are investigated and some numerical experiments are proposed.     

Positive solutions to semi-positone fourth-order $$\phi $$-Laplacian BVPs

This work is devoted to proving existence of positive solutions to a fourth-order semipositone \(\phi \)-Laplacian boundary problem. The nonlinearity may have time-singularity and change sign. Existence results are proved using the Krasnosel’skii and the Leggett-Williams fixed point theorems and examples of applications are provided.     

A q-analogue for binomial coefficients and generalized Fibonacci sequences

A new q-analogue of bi^snomial coefficients is proposed according to the generalized q-Fibonacci sequence suggested by Cigler's approach.