Let be a complete metric space, and be a -weak or generalized -weak contraction mapping, where are two mappings with , , if and is continuous or is monotone nondecreasing with for all . Then has a unique fixed point. Our results extend the previous results given by Rhoades (2001) [3], Dutta and Choudhury (2008) [4], Doric (2009) [5] and Popescu (2011) [6].
