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Some new results on fixed and best proximity points in preordered metric spaces. (English) Zbl 1469.54054

Summary: In this paper, we first introduce two new classes of \((\omega, \delta)\)-contractions of the first and second kinds and establish some related new fixed point and best proximity point theorems in preordered metric spaces. Our theorems subsume the corresponding recent results of B. Samet [J. Optim. Theory Appl. 159, No. 1, 281–291 (2013; Zbl 1292.90317)] and extend and generalize many of the well-known results in the literature. An example is also provided to support our main results.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces

Citations:

Zbl 1292.90317
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References:

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