A unuqueness theorem for Sturm-Lioville operators with eigenparameter dependent boundary conditions

In this paper, we discuss the inverse problem for Sturm- Liouville operators with boundary conditions having fractional linear function of spectral parameter on the finite interval $[0, 1].$ Using Weyl m-function techniques, we establish a uniqueness theorem. i.e., If q(x) is prescribed on $[0,frac{1}{2}+alpha]$ for some $alphain [0,1),$ then the potential $q(x)$ on the interval $[0, 1]$ and fractional linear function $frac{a_2lambda+b_2}{c_2lambda+d_2}$ of the boundary condition are uniquely determined by a subset $Ssubset sigma (L)$ and fractional linear function $frac{a_1lambda+b_1}{c_1lambda+d_1}$ of the boundary condition.