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On generalized weakly directional contractions and approximate fixed point property with applications. (English) Zbl 1281.54022

Summary: In this article, we first introduce the concept of directional hidden contractions in metric spaces. The existences of generalized approximate fixed point property for various types of nonlinear contractive maps are also given. From these results, we present some new fixed point theorems for directional hidden contractions which generalize Berinde-Berinde’s fixed point theorem [M. Berinde and V. Berinde, J. Math. Anal. Appl. 326, No. 2, 772–782 (2007; Zbl 1117.47039)], Mizoguchi-Takahashi’s fixed point theorem [N. Mizoguchi and W. Takahashi, J. Math. Anal. Appl. 141, No. 1, 177–188 (1989; Zbl 0688.54028)] and some other well-known results in the literature.

MSC:

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