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Optimal approximate solution for \(\alpha\)-multiplicative proximal contraction mappings in multiplicative metric spaces. (English) Zbl 1342.54030

Summary: In this work, we introduce the new concept of \(\alpha \)-multiplicative proximal contraction mappings in the setting of multiplicative metric spaces and we also solve optimal approximate solution for such mappings. Our main results improve and extend several results in the literature. We also state some illustrative examples to claim that our results properly generalizes some results in literature.

MSC:

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

[1] Bashirov AE, Kurpinar EM, Özyapici A (2008) Multiplicative calculus and its applications. J Math Anal Appl 337:36-48 · Zbl 1129.26007 · doi:10.1016/j.jmaa.2007.03.081
[2] Özavşar M, Çevikel AC (2012) Fixed points of multiplicative contraction mappings on multiplicative metric spaces, Math GN: 23 May 2012 · Zbl 1437.54059
[3] Mongkolkeha C, Sintunavarat W (2015) Best proximity points for multiplicative proximal contraction mapping on multiplicative metric spaces. J Nonlinear Sci Appl 8:1134-1140 · Zbl 1437.54059
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