### Some Fixed Point Theorems for Expansive Mappings in Cone Pentagonal Metric Spaces

#### Abstract

In this paper, we prove some xed point theorems for mappings satisfying expansive conditions in non-normal cone pentagonal metric spaces. Our results extend and improve the recent results announced by Patil and Salunke [Fixed point theorems for Expansion mappings in Cone rectangular metric spaces, Gen. Math. Notes, 29(1), (2015), 30-39], Shatanawi and Awawdeh, [Some xed and coincidence point theorems for Expansive maps in Cone metric spaces, Fixed Point Theory and Applications, 1(2012), 1-10], Huang, Zhu and Wen, [Fixed point theorems for Expanding mappings in Cone metric spaces, Math. Reports 14(64), 2(2012), 141-148], Kadelburg, Murthy and Radenovic, [Common xed points for Expansive mappings in Cone metric spaces, Int. J. Math. Anal, 5(27), (2011), 1309-1319], Aage and Salunke, [Some xed point theorems for Expansion onto mappings on Cone metric spaces, Acta Mathematica Sinica, 27(6), (2011), 1101-1106], Kumar and Garg, [Common xed points for Expansion mappings Theorems in metric spaces, Int. J. Contemp. Math. Sciences, 4(36), (2009), 1749-1758], and many others in the literature.

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DOI: http://dx.doi.org/10.26713%2Fjims.v9i1.581

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