锥度量空间上混合型膨胀映射族的唯一公共不动点

朴勇杰

数学学报 ›› 2014, Vol. 57 ›› Issue (6) : 1041-1046.

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数学学报 ›› 2014, Vol. 57 ›› Issue (6) : 1041-1046. DOI: 10.12386/A2014sxxb0096
论文

锥度量空间上混合型膨胀映射族的唯一公共不动点

    朴勇杰
作者信息 +

Unique Common Fixed Points for Mixed Type Expansion Mappings on Cone Metric Spaces

    Yong Jie PIAO
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摘要

引进了一类混合型膨胀映射族,并在锥度量空间上证明了此类映射族具有唯一公共不动点的定理,同时给出了相应的不动点定理,推广和改进了文献中关于第I膨胀映射的相应的公共不动点和不动点定理.

Abstract

A new type of expansion mappings is introduced, and that this type mappings have a unique common fixed point is proved on cone metric spaces, and then the corresponding unique fixed point results are given.The main results generalize and improve the corresponding common fixed points and fixed points theorems for I-expansion mappings in references.

关键词

锥度量空间 / 混合型膨胀映射 / 重合点 / 公共不动点 / 不动点

Key words

cone metric space / mixed type expansion mapping / coincident point / common fixed point / fixed point

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朴勇杰. 锥度量空间上混合型膨胀映射族的唯一公共不动点. 数学学报, 2014, 57(6): 1041-1046 https://doi.org/10.12386/A2014sxxb0096
Yong Jie PIAO. Unique Common Fixed Points for Mixed Type Expansion Mappings on Cone Metric Spaces. Acta Mathematica Sinica, Chinese Series, 2014, 57(6): 1041-1046 https://doi.org/10.12386/A2014sxxb0096

参考文献

[1] Bari C.D., Vetro P., φ-pair and common fixed points in cone metric spaces, Rendiconti del Circolo Mathematico Palermo, 2008, 57: 279-285.

[2] He N.S., Fixed point theorems on II, III type expansive mappings (in Chinese), J.Civil Aviation Univ.of China, 2004, 22(5): 50-52.

[3] He N.S., A fixed point theorems on the weak expansion mappings (in Chinese), J.Nanjing University Math. Biquarterly, 2006, 23(2): 334-340.

[4] Huang L.G., Zhang X., Cone metric spaces and fixed point theorems of contractive mappings, J.Math. Anal.Appl., 2007, 332(2): 1468-1476.

[5] Kadelburg Z., Murthy P.P., Radenóvic S., Common fixed points for expansive mappings in cone metric spaces, Int.J.Math.Analysis, 2011, 5(27): 1309-1319.

[6] Piao Y.J., Jin Y.F., New unique common fixed point results for four mappings with Φ-contractive type in 2-metric spaces, Applied Math., 2012, 3(7): 734-737.

[7] Sahin I.Telci M., A theorem on common fixed points of expansion type mappings in cone metric spaces, An. St.Univ.Ovidius Constanta, 2010, 18(1): 329-336.

[8] Shatanawi W., Awawdeh F., Some fixed and coincidence point theorems for expansive maps in cone metric spaces, Fixed Point Theory Appl., 2012, doi:10.1186/1687-1812-2012-19.

[9] Wang S.Z., Li B Y., Gao Z.M., Expansive mappings and fixed point theorems (in Chinese), Advances in Mathematics, 1982, 11(2): 149-153.

[10] Zhang X., Common fixed point theorem of Lipschitz type mappings on cone metric spaces, Acta Mathematica Sinica, Chinese Series, 2010, 53(6): 1139-1148.

基金

国家自然科学基金(11261062, 11361064);吉林省教育厅科研项目(吉教科合字[2011]第434号)

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