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

Authors

  • Abba Auwalu Department of Mathematics, Near East University, Nicosia-TRNC, Mersin 10
  • Evren Hincal Department of Mathematics, Near East University, Nicosia-TRNC, Mersin 10

DOI:

https://doi.org/10.26713/jims.v9i1.581

Keywords:

Cone pentagonal metric spaces, Common fixed point, Expansive maps, Weakly compatible maps

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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Author Biographies

Abba Auwalu, Department of Mathematics, Near East University, Nicosia-TRNC, Mersin 10

Lecturer, Department of Mathemetics, Near East University, Nicosia

Evren Hincal, Department of Mathematics, Near East University, Nicosia-TRNC, Mersin 10

Head, Department of Mathemetics, Near East University, Nicosia

References

M. Abbas and G. Jungck, Common xed point results for non commuting mappings without continuity in cone metric spaces, J. Math. Anal. and Appl., 341 (2008), 416 - 420.

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S. Z. Wang, B. Y. Li, Z. M. Gao and K. Iseki, Some fixed point theorems for expansion mappings, Math. Jpn., 29 (1984), 631 - 636.

P. Z. Daer and H. Kaneko, On expansive mappings, Math. Jpn., 37 (1992), 733 - 735.

C T. Aage and J N. Salunke, Some fixed point theorems for Expansion onto mappings on Cone metric spaces, Acta Mathematica Sinica, 27(6), (2011), 1101 - 1106.

W. Shatanawi and F. Awawdeh, Some fixed and coincidence point theorems for Expansive maps in Cone metric spaces, Fixed Point Theory and Applications, 1(2012), 1 - 10.

Z. Kadelburg, P.P. Murthy and S. Radenovic, Common fixed points for Expansive mappings in Cone metric spaces, Int. J. Math. Anal, 5(27), (2011), 1309 - 1319.

X. Huang, Ch. Zhu and X. Wen, Fixed point theorems for Expanding mappings in Cone metric spaces, Math. Reports 14(64), 2(2012), 141 - 148.

S.R. Patil1 and J.N. Salunke Fixed point theorems for Expansion mappings in Cone rectangular metric spaces, Gen. Math. Notes, 29(1), (2015), 30 - 39.

S. Kumar and S.K. Garg, Common fixed points for Expansion mappings Theorems in metric spaces, Int. J. Contemp. Math. Sciences, 4(36), (2009), 1749 - 1758.

G. Jungck, S. Radenovic, S. Radojevic, and V. Rakocevic, Common fixed point theorems for weakly compatible pairs on cone metric spaces, Fixed Point Theory and Applications, 2009. http://dx.doi.org/10.1155/2009/643840

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Published

2017-06-09
CITATION

How to Cite

Auwalu, A., & Hincal, E. (2017). Some Fixed Point Theorems for Expansive Mappings in Cone Pentagonal Metric Spaces. Journal of Informatics and Mathematical Sciences, 9(1), 111–122. https://doi.org/10.26713/jims.v9i1.581

Issue

Vol. 9 No. 1 (2017)

Section

Research Articles

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