Generalized weak contractions in partially ordered metric spaces

Recent results of Đorić [D. Đorić, Common fixed point for generalized (ψ,φ)(ψ,φ)-weak contractions, Appl. Math. Lett. 22 (2009) 1896–1900] on generalized weakly contractive mappings are extended to the setting of partially ordered metric spaces. Thus, generalization of fixed point results of Harjani and Sadarangani [J. Harjani, K. Sadarangani, Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Anal. 71 (2009) 3403–3410] is obtained. Some applications are presented. Examples are given to show that our results are proper generalizations of the existing ones.