α-(h,e)-convex operators and applications for Riemann-Liouville fractional differential equations - Zhou, Bibo; Zhang, Lingling (Topological Methods in Nonlinear Analysis, 2023)
In this paper, we consider a class of α-(h,e)-convex operators defined in set P_h,e and applications with α> 1. Without assuming the operator to be completely continuous or compact, by employing cone theory and monotone iterative technique, we not only obtain the existence and uniqueness of fixed point of α-(h,e)-convex operators, but also construct two monotone iterative sequences to approximate the unique fixed point. At last, we investigate the existence-uniqueness of a nontrivial solution for Riemann-Liouville fractional differential equations integral boundary value problems by employing α-(h,e)-convex operators fixed point theorem.