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Generalized weak contractions in partially ordered metric spaces. (English) Zbl 1202.54039
Summary: Recent results of D. Dorić [Appl. Math. Lett. 22, No. 12, 1896–1900 (2009; Zbl 1203.54040)] 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.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
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