Best proximity points for generalized proximal weak contractions satisfying rational expression on ordered metric spaces. (English) Zbl 1351.54030

Pragadeeswarar, V.; Marudai, M.

Abstr. Appl. Anal. 2015, Article ID 361657, 6 p. (2015).

Summary: We introduce a generalized proximal weak contraction of rational type for the non-self-map and proved results to ensure the existence and uniqueness of best proximity point for such mappings in the setting of partially ordered metric spaces. Further, our results provides an extension of a result due to Nguyen Van Luong and Nguyen Xuan Thuan [Fixed Point Theory Appl. 2011, Article ID 46, 10 p. (2011; Zbl 1315.54040)] and also it provides an extension of [J. Harjani et al., Abstr. Appl. Anal. 2010, Article ID 190701, 8 p. (2010; Zbl 1203.54041)] to the case of self-mappings.

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 1315.54040; Zbl 1203.54041

References:

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