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Fixed point theorems for generalized weakly contractive mappings in metric spaces with applications. (English) Zbl 1462.54047

Summary: In this paper, motivated and inspired by B. Samet et al. [ibid. 2013, Paper No. 5, 11 p. (2013; Zbl 1285.54043)], we introduce the notion of generalized weakly contractive mappings in metric spaces and prove the existence and uniqueness of fixed point for such mappings, and we obtain a coupled fixed point theorem in metric spaces. These theorems generalize many previously obtained fixed point results. An example is given to illustrate the main result. Finally, we give applications of our results to fixed point results in partial metric spaces.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces

Citations:

Zbl 1285.54043
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References:

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