×

zbMATH — the first resource for mathematics

A note on ‘\(\psi\)-Geraghty type contractions’. (English) Zbl 1395.54049
Summary: Very recently, the notion of a \(\psi\)-Geraghty type contraction was defined by M. E. Gordji et al. [ibid. 2012, Paper No. 74, 9 p. (2012; Zbl 1278.54031)]. In this short note, we realize that the main result via \(\psi\)-Geraghty type contraction is equivalent to an existing related result in the literature. Consequently, all results inspired by the paper of Gordji et al. [loc. cit.] can be derived in the same way.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Geraghty, M, On contractive mappings, Proc. Am. Math. Soc, 40, 604-608, (1973) · Zbl 0245.54027
[2] Amini-Harandi, A; Emami, H, A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal., Theory Methods Appl, 72, 2238-2242, (2010) · Zbl 1197.54054
[3] Amini-Harandi, A; Fakhar, M; Hajisharifi, H; Hussain, N, Some new results on fixed and best proximity points in preordered metric spaces, No. 2013, (2013) · Zbl 06334843
[4] Bilgili, N; Karapinar, E; Sadarangani, K, A generalization for the best proximity point of Geraghty-contractions, No. 2013, (2013) · Zbl 1281.54020
[5] Mongkolkeha, C; Cho, Y; Kumam, P, Best proximity points for geraghty’s proximal contraction mappings, No. 2013, (2013) · Zbl 06320812
[6] Kim, J; Chandok, S, Coupled common fixed point theorems for generalized nonlinear contraction mappings with the mixed monotone property in partially ordered metric spaces, No. 2013, (2013) · Zbl 06334799
[7] Karapinar, E, On best proximity point of \(ψ\)-Geraghty contractions, No. 2013, (2013) · Zbl 1295.41037
[8] Caballero, J; Harjani, J; Sadarangani, K, A best proximity point theorem for Geraghty-contractions, No. 2012, (2012) · Zbl 1281.54021
[9] Abbas, M; Sintunavarat, W; Kumam, P, Coupled fixed point of generalized contractive mappings on partially ordered \(G\)-metric spaces, No. 2012, (2012) · Zbl 06208283
[10] Sintunavarat, W: Generalized Ulam-Hyers stability, well-posedness and limit shadowing of fixed point problems for [InlineEquation not available: see fulltext.]-contraction mapping in metric spaces. Sci. World J. (in press)
[11] Cho, S-H; Bae, J-S; Karapinar, E, Fixed point theorems for \(α\)-Geraghty contraction type maps in metric spaces, No. 2013, (2013) · Zbl 1423.54073
[12] Gordji, ME; Ramezani, M; Cho, YJ; Pirbavafa, S, A generalization of geraghty’s theorem in partially ordered metric spaces and applications to ordinary differential equations, No. 2012, (2012) · Zbl 1278.54031
[13] Raj, VS, A best proximity theorem for weakly contractive non-self mappings, Nonlinear Anal, 74, 4804-4808, (2011) · Zbl 1228.54046
[14] Raj, VS: Banach’s contraction principle for non-self mappings (preprint)Raj, VS: Banach’s contraction principle for non-self mappings (preprint) · Zbl 1297.54076
[15] Abkar, A; Gabeleh, M, A note on some best proximity point theorems proved under \(P\)-property, No. 2013, (2013) · Zbl 1297.54076
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.