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Some results on fixed points of α-ψ-Ciric generalized multifunctions

DOI: 10.1186/1687-1812-2013-24

Keywords: α-ψ-Ciric generalized multifunction, fixed point, quasi-contractive multifunction

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Abstract:

In 2012, Samet, Vetro and Vetro introduced α-ψ-contractive mappings and gave some results on a fixed point of the mappings (Samet et al. in Nonlinear Anal. 75:2154-2165, 2012). In fact, their technique generalized some ordered fixed point results (see (Alikhani et al. in Filomat, 2012, to appear) and (Samet et al. in Nonlinear Anal. 75:2154-2165, 2012)). By using the main idea of (Samet et al. in Nonlinear Anal. 75:2154-2165, 2012), we give some new results for α-ψ-Ciric generalized multifunctions and some related self-maps. Also, we give an affirmative answer to a recent open problem which was raised by Haghi, Rezapour and Shahzad in 2012.

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