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This study aims to obtain a lower bound on the eigenvalue of the smallest modulus in a general weighted regular Sturm-Liouville problem with mixed boundary conditions. The problem is expressed as -u′′(x) + q(x)u(x) = λr(x)u(x) over the interval [a,b] with u′(a) = u(b) = 0. In 1988 Mingarelli [31]...

A commutatively ordered Banach algebra (COBA) is a complex unital Banach algebra A containing a subset C, called an algebra c-cone, such that C contains the unit of A and is closed under addition, positive scalar multiplication and multiplication by commuting positive elements. If the...