This paper deals with the boundary value problem involving the differential equation \begin{equation}\label{1} \ell y:=-y''+qy=\lambda y, \end{equation} subject to the parameter dependent boundary conditions \begin{align}\label{2} &L_1(y):=\lambda\left(y'(0)+h_1 y(0)\right)-h_2y'(0)-h_3y(0)= 0, \nonumber\\ & L_2(y):=\lambda\left(y'(\pi)+ H_1y(\pi)\right)-H_2 y'(\pi)-H_3y(\pi) =0, \end{align} along with the following discontinuity conditions at the points $d_i\in (0,\pi)$ \begin{align}\label{3} U_{i}(y)&:= y(d_i+0)- a_iy(d_i-0)=0, \nonumber \\ V_{i}(y)&:=y'(d_i+0)-b_iy'(d_i-0)-c_i y(d_i-0)=0,\ \end{align} where $q(x), \ a_i ,\ b_i,\ c_i$, `for $i=1,2,\cdots, m$' are real, $q\in L^{2}(0,\pi)$ and $\lambda$ is a parameter independent of $x$. For simplicity we use the notation $L=L(q(x); h_j;H_j;d_i)$, for the problem \eqref{1}--\eqref{3}. We develop the Hochstadt's result [1] based on the transformation operator for inverse Sturm-Liouville problem when there are finite number of transmission and parameter dependent conditions [2]. Furthermore, we establish a formula for $q(x) - \tilde{q}(x)$ in the finite interval where $q(x)$ and $\tilde{q}(x)$ are analogous functions.
