The present study focusses on the existence of positivity of the solutions to the higher order three-point boundary value problems involving $p$-Laplacian
\[
[\phi_p(x^{(m)}(t))]^{(n)} = g(t, x(t)), \quad t \in [0,1],
\]
\[
x^{(i)}(0) = 0, \quad \text{for } 0 \le i \le m-2,
\]
\[
x^{(m-2)}(1) – \alpha x^{(m-2)}(\xi) = 0,
\]
\[
[\phi_p(x^{(m)}(t))]^{(j)}\big|_{t=0} = 0, \quad \text{for } 0 \le j \le n-2,
\]
\[
[\phi_p(x^{(m)}(t))]^{(n-2)}\big|_{t=1} – \alpha [\phi_p(x^{(m)}(t))]^{(n-2)}\big|_{t=\xi} = 0,
\]
where $m,n \ge 3$, $\xi \in (0,1)$, $\alpha \in \left(0, \frac{1}{2}\right)$ is a parameter.
The approach used by the application of Guo–Krasnosel’skii fixed point theorem to determine the existence of positivity of the solutions to the problem.