TY - JOUR
AU - Zhou, Bibo
AU - Zhang, Lingling
PY - 2023/02/26
Y2 - 2024/09/13
TI - $\alpha$-$(h,e)$-convex operators and applications for Riemann-Liouville fractional differential equations
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 61
IS - 2
SE -
DO - 10.12775/TMNA.2022.014
UR - https://apcz.umk.pl/TMNA/article/view/42811
SP - 577 - 590
AB - In this paper, we consider a class of $\alpha$-$(h,e)$-convex operators defined in set $P_{h,e}$ and applications with $\alpha> 1$. Without assuming the operatorto be completely continuous or compact, by employing cone theory and monotone iterative technique, we not only obtain the existence and uniqueness of fixed pointof $\alpha$-$(h,e)$-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$\alpha$-$(h,e)$-convex operators fixed point theorem.
ER -