In this work a new functional expansion-compression fixed point theorem of Leggett--Williams type is developed for a class of mappings of the form $T+F,$ where $(I-T)$ is Lipschitz invertible map and $F$ is a $k$-set contraction. The arguments are based upon recent fixed point index theory in cones of Banach spaces for this class of mappings. As application, our approach is applied to prove the existence of nontrivial nonnegative solutions for three-point boundary value problem.
Fixed point index, cone, sum of operators, Green's function, positive solution
MOUHOUS, AMIROUCHE and MEBARKI, KARIMA
"Existence of fixed points in conical shells of a Banach space for sum of two operators and application in ODEs,"
Turkish Journal of Mathematics: Vol. 46:
7, Article 2.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss7/2