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### Fixed Point Theorems For A Class Of Nonlinear Sum-type Operators And Application In A Fractional Differential Equation

 Title: Name(s): Fixed Point Theorems For A Class Of Nonlinear Sum-type Operators And Application In A Fractional Differential Equation. 11 views 0 downloads Wang, Hui, authorZhang, Lingling, authorWang, Xiaoqiang, author text Journal ArticleTextJournal Article 2018-09-18 computeronline resource 1 online resource English In this paper, we consider the fixed point for a class of nonlinear sum-type operators 'A +B+ C' on an ordered Banach space, where A, B are two mixed monotone operators, C is an increasing operator. Without assuming the existence of upper-lower solutions or compactness or continuity conditions, we prove the unique existence of a positive fixed point and also construct two iterative schemes to approximate it. As applications, we research a nonlinear fractional differential equation with multi-point fractional boundary conditions. By using the obtained fixed point theorems of sum-type operator, we get the sufficient conditions which guarantee the existence and uniqueness of positive solutions. At last, a specific example is provided to illustrate our result. FSU_libsubv1_wos_000446257800001 (IID), 10.1186/s13661-018-1059-y (DOI) boundary-value-problems, convex, existence, Existence and uniqueness, Fractional boundary condition, Fractional differential equation, mixed monotone-operators, Positive solution, positive solutions, Sum-type operator, uniqueness The publisher’s version of record is available at https://doi.org/10.1186/s13661-018-1059-y http://purl.flvc.org/fsu/fd/FSU_libsubv1_wos_000446257800001 FSU Boundary Value Problems.1687-2770

Wang, H., Zhang, L., & Wang, X. (2018). Fixed Point Theorems For A Class Of Nonlinear Sum-type Operators And Application In A Fractional Differential Equation. Boundary Value Problems. Retrieved from http://purl.flvc.org/fsu/fd/FSU_libsubv1_wos_000446257800001