in this work, by employing the krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime...

t regulatory cells play a crucial role in immunological unresponsiveness to self- antigens and in suppressing excessive immune responses deleterious to the host. t regulatory cells are produced in the thymus as a functionally mature subpopulation of t cells. they can be induced from naive t cells in the periphery and express their marker as a forkhead/winged helix transcription factor called fo...