On fixed points of pointwise Lipschitzian type mappings

摘要

The classes of pointwise Lipschitzian type mappings and asymptotic pointwise Lipschitzian type mappings are introduced and their properties are discussed. The existence of fixedpoints for pointwise Lipschitzian type mappings and asymptotic pointwise Lipschitzian type mappings are investigated in Banach spaces. Our results generalize and improve the corresponding resultsof L.P. Belluce and W.A. Kirk [Fixed point theorems for certain classes of nonexpansive mappings,Proc. Amer. Math. Soc., 20 (1969) 141-146]; E. Casini and E. Maluta [Fixed points of uniformlyLipschitzian mappings in spaces with uniformly normal structure, Nonlinear Anal., 9 (1985), 103-108]; K. Goebel and W.A. Kirk [A fixed point theorem for asymptotically nonexpansive mappings,Proc. Amer. Math. Soc., 35 (1972), 171-174]; W.A. Kirk and H.K. Xu [Asymptotic pointwise contractions, Nonlinear Anal., 69 (2008), 4706-4712]; and T.C. Lim and H.K. Xu [Fixed point theoremsfor asymptotically nonexpansive mappings, Nonlinear Anal., 22(11) (1994), 1345-1355].