LAUSR

Let be an interval and a strictly increasing and continuous function with a unique fixed point that satisfies for all , where the equality holds only when . The general quantum operator defined by Hamza et al., if and if generalizes the Jackson q-operator and also the Hahn (quantum derivative) operator, . Regarding a β-Sturm–Liouville eigenvalue problem associated with the above operator , we construct the β-Lagrange's identity, show that it is self-adjoint in and exhibit some properties for the corresponding eigenvalues and eigenfunctions.