The common fixed point of single-valued generalized -weakly contractive mappings

Fixed point and coincidence results are presented for single-valued generalized φ f -weakly contractive mappings on complete metric spaces ( X , d ) , where φ : [ 0 , ∞ ) → [ 0 , ∞ ) is a lower semicontinuous function with φ ( 0 ) = 0 and φ ( t ) > 0 for all t > 0 and f : E → X is a function such that E ⊆ X is nonempty and closed. Our results extend previous results given by Rhoades (2001) [1] and by Zhang and Song (2009) [2].