In the present paper, the authors prove some fixed point theorems for generalized nonlinear contractive type mappings on complete partial metric spaces, including a Banach type fixed point theorem due to S. G. Matthews
[Partial metric topology. Andima, Susan (ed.) et al., Papers on general topology and applications. Papers from the 8th summer conference at Queens College, New York, NY, USA, June 18–20, 1992. New York, NY: The New York Academy of Sciences. Ann. N. Y. Acad. Sci. 728, 183–197 (1994: Zbl 0911.54025
)]. Moreover, a homotopy result on fixed points is given.