fixed point theorem on functional intervals for sum of two operators and application in odes

In this paper, we present a generalization of the functional expansion-compression fixed point theorem developed by avery et al. in [5] to the case of a k-set contraction perturbed by an operator t, where i -t is lipschitz invertible. the arguments are based upon recent fixed point index theory in cones of banach spaces. next, we apply the obtained result to discuss the existence of a nontrivial positive solution to a nonautonomous second order boundary value problem.