Fixed point theorems of superlinear operators with applications (Q2672489)

The authors prove fixed point theorems for special classes of nonlinear operators between Banach spaces and apply them to existence and uniqueness results for Hammerstein integral equations. Similar notions and results have been obtained under the name mixed monotone operators by many authors in previous papers, e.g., by \textit{H. Afshari} et al. [Filomat 31, No. 9, 2675--2682 (2017; Zbl 1488.34165)], \textit{J. Caballero} et al. [J. Math. Anal. Appl. 305, No. 1, 304--315 (2005; Zbl 1076.45002)], \textit{J. R. Graef} et al. [Fract. Differ. Calc. 2, No. 1, 87--98 (2012; Zbl 1412.34086)], \textit{M. Jleli} and \textit{B. Samet} [Nonlinear Anal., Model. Control 20, No. 3, 367--376 (2015; Zbl 1420.34018)], \textit{C. Zhai} and \textit{M. Hao} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 4, 2542--2551 (2012; Zbl 1253.47037)], and \textit{X. Zhang} [Appl. Math. Lett. 39, 22--27 (2015; Zbl 1387.34014)]).