LIU Li-ya, GU Feng. A New Coupled Common Fixed Point Theorem for Square Contractive Mappings in 2-Metric Spaces[J]. Applied Mathematics and Mechanics, 2017, 38(8): 956-966. doi: 10.21656/1000-0887.370261
Citation: LIU Li-ya, GU Feng. A New Coupled Common Fixed Point Theorem for Square Contractive Mappings in 2-Metric Spaces[J]. Applied Mathematics and Mechanics, 2017, 38(8): 956-966. doi: 10.21656/1000-0887.370261

A New Coupled Common Fixed Point Theorem for Square Contractive Mappings in 2-Metric Spaces

doi: 10.21656/1000-0887.370261
Funds:  The National Natural Science Foundation of China(11071169)
  • Received Date: 2016-08-30
  • Rev Recd Date: 2016-10-16
  • Publish Date: 2017-08-15
  • In the framework of 2-metric spaces, a new class of square contractive conditions were established and the existence and uniqueness of the coupled common fixed point in given conditions were discussed, by means of the ω-compatible condition for the pair of mappings. Then a new coupled common fixed point theorem was proved. Several illustrative examples were also given in support of the new theorem. The work improves the relative results in the recent literatures.
  • loading
  • [1]
    GU Feng, YIN Yun. A new common coupled fixed point theorem in generalized metric space and applications to integral equations[J].Fixed Point Theory and Applications,2013,2013(1): 266.
    [2]
    Aghajani A, Arab R. Fixed points of (ψ,φ,θ)-contractive mappings in partially orderedb -metric spaces and application to quadratic integral equations[J].Fixed Point Theory and Applications,2013,2013(1): 245.
    [3]
    ZHU Chuan-xi, XU Wen-qing, CHEN Chun-fang, et al. Common fixed point theorems for generalized expansive mappings in partial b-metric spaces and an application[J].Journal of Inequalities and Applications,2014,2014(1): 475.
    [4]
    Mustafa Z, Parvaneh V, Roshan J R, et al.b-2-metric spaces and some fixed point theorems[J].Fixed Point Theory and Applications,2014,2014(1): 144.
    [5]
    Fathollahi S, Hussain N, Khan L A. Fixed point results for modified weak and rational α-ψ-contractions in ordered 2-metric spaces[J].Fixed Point Theory and Applications,2014,2014(1): 6.
    [6]
    Ghler S. 2-metrische Rume und ihre topogische Struktur[J].Mathematische Nachrichten,1963,26(1/4): 115-148.
    [7]
    Iséki K. Fixed point theorems in 2-metric spaces[J].Math Seminar Notes, Kobe, Univ,1975,3(1): 133-136.
    [8]
    Deshpande B, Chouhan S. Common fixed point theorems for hybrid pairs of mappings with some weaker conditions in 2-metric spaces[J].Fasc Math,2011(46): 37-55.
    [9]
    Aliouche A, Simpson C. Fixed points and lines in 2-metric spaces[J].Advances in Mathematics,2012,229(1): 668-690.
    [10]
    Lahiri B K, Das P, Dey L K. Cantor’s theorem in 2-metric spaces and its applications to fixed point problems[J].Taiwan J Math,2011,15(1): 337-352.
    [11]
    LIU Ze-qing, ZHANG Feng-rong. Characterizations of common fixed points in 2-metric space[J]. Rostock Math Kolloq,2001,55(1): 49-64.
    [12]
    Dung N V, Hieu N T, Ly N T T, et al. Remarks on the fixed point problem of 2-metric spaces[J]. Fixed Point Theory and Applications,2013,2013(1): 167.
    [13]
    Dung N V, Le Hang V T. Fixed point theorems for weak C-contractions in partially ordered 2-metric spaces[J].Fixed Point Theory and Applications,2013,2013(1): 161.
    [14]
    Dubey R P. Some fixed point theorems on expansion mappings in 2-metric spaces[J].Pure Appl Math Sci,1990,32(1/2): 33-37.
    [15]
    张石生. 不动点理论及其应用[M]. 重庆: 重庆出版社, 1984. (ZHANG Shi-sheng.Fixed Point Theory and Application[M]. Chongqing: Chongqing Press,1984.(in Chinese))
    [16]
    Bhaskar T G, Lakshmikantham V. Fixed point theorems in partially ordered metric spaces and applications[J].Nonlinear Analysis: Theory, Methods & Applications,2006,65(7): 1379-1393.
    [17]
    Lakshmikantham V, Ciric L B. Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces[J].Nonlinear Analysis: Theory, Methods & Applications,2009,70(12): 4341-4349.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (686) PDF downloads(502) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return