Fixed point results on nonlinear composition operators A∘B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$A\circ B$\end{document} and applications

This paper investigates a class of composition operators: the nonlinear operator T=A∘B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$T=A\circ B$\end{document} and the sum-type operator T=A∘B+C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$T=A\circ B+C$\end{document}, where A, B, and C are either single or bivariate operators. Here, “∘” denotes the composition operation between operators A and B. By applying cone theory and monotone iterative techniques, we establish the existence and uniqueness of fixed points of T within the set P. Additionally, we develop two successively monotone iterative sequences to approximate the unique positive fixed point. Finally, by leveraging the fixed point theorem for composition operators derived in this paper, we analyze a class of boundary value problems for Riemann-Liouville fractional differential equations involving p-Laplacian operators.