On fixed points of pointwise Lipschitzian type mappings (Q2871109)

From the abstract: The classes of pointwise Lipschitzian type mappings and asymptotic pointwise Lipschitzian type mappings are introduced and their properties are discussed. The existence of fixed points for pointwise Lipschitzian type mappings and asymptotic pointwise Lipschitzian type mappings in Banach spaces is investigated. Our results generalize and improve the corresponding results of \textit{L. P. Belluce} and \textit{W. A. Kirk} [Proc. Am. Math. Soc. 20, 141--146 (1969; Zbl 0165.16801)]; \textit{E. Casini} and \textit{E. Maluta} [Nonlinear Anal., Theory Methods Appl. 9, 103--108 (1985; Zbl 0526.47034)]; \textit{K. Goebel} and \textit{W. A. Kirk} [Proc. Am. Math. Soc. 35, 171--174 (1972; Zbl 0256.47045)]; \textit{W. A. Kirk} and \textit{H.-K. Xu} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 69, No. 12, 4706--4712 (2008; Zbl 1172.47038)]; \textit{T.-C. Lim} and \textit{H.-K. Xu} [Nonlinear Anal., Theory Methods Appl. 22, No. 11, 1345--1355 (1994; Zbl 0812.47058)].