GONG Xue,XU Jianing,WU Fan,et al.Unique common fixed points for a family of mappings with contractive type conditions on complete D-metric spaces[J].Journal of Yanbian University,2015,41(01):1-4.
完备的D-度量空间上具有收缩型条件映射族的唯一公共不动点
- Title:
- Unique common fixed points for a family of mappings with contractive type conditions on complete D-metric spaces
- 分类号:
- O177.3; O189.11
- 文献标志码:
- A
- 摘要:
- 利用完备的D-度量空间上满足某种收缩条件的4个自映射S,T,I,J构造了具有唯一极限的序列,并证明了该序列的唯一极限即为S,T,I,J的唯一公共不动点,且由此得到了更为一般形式的无穷多个映射的唯一公共不动点定理,所得结果推广和改进了D-度量空间上的若干唯一公共不动点定理.
- Abstract:
- We use four self-mappings S, T, I, J satisfying some contractive conditions on complete D-metric spaces to construct a sequence which has a unique limit, and prove that the unique limit of the sequence is the unique common fixed point of S, T, I, J. Furthermore, we obtain a more general unique common fixed point theorem for an infinite family of self-mappings. The obtained results generalize and improve some unique common fixed point theorems on D-metric spaces.
参考文献/References:
[1] Dhage B. Generalized metric spaces and mappings with fixed points[J]. Bulletin of Calcutta Mathematical Society, 1992,84(4):329-336.
[2] Singh B, Jain S, Jain S. Semicompatibility and fixed point theorems in an unbounded D-metric space[J]. International Journal of Mathematics and Mathematical Science, 2005,2005(5):789-801.
[3] Dhage B, Arya S, Ume J. A general lemma for fixed point theorems involving more than two maps in D-metric spaces with applications[J]. International Journal of Mathematics and Mathematical Science, 2003,2003(11):661-672.
[4] Dhage B, Asha A, Kang S. On common fixed points of pairs of a single and a multivalued coincidentally commuting mappings in D-metric spaces[J]. International Journal of Mathematics and Mathematical Science, 2003,2003(40):2519-2539.
[5] Singh B, Jain S. Common fixed points of weak-compatible maps on D-metric space[J]. Journal of ChungCheong Mathematical Society, 2004,17(2):111-124.
[6] Singh B, Sharma R. Common fixed points via compatible maps in D-metric spaces[J]. Rad Mat, 2002,11(2):145-153.
[7] Gajic’ L. On a common fixed point for sequence of selfmappings in generalized metric space[J]. Novi Sad J Math, 2006,36(2):153-156.
[8] 沈京虎,朴勇杰.D-度量空间上一族拟收缩自映射的唯一公共不动点[J].延边大学学报:自然科学版,2014,40(1):8-10.
[9] Abbas M, Jungck G. Common fixed point results for noncommuting mappings without continuity in cone metric spaces[J]. Journal of Mathematical Analysis and Applications, 2006,341(1):416-420.
[10] Han Y, Xu S Y. New common fixed point results for four maps on cone metric spaces[J]. Applied Mathematics, 2011,2:1114-1118.
[11] Bari C D, Vetro P. φ-pairs and common fixed points in cone metric spaces[J]. Rendiconti del circolo Matematico Palermo, 2008,57:279-285.
[12] Dhage B. Some results on common fixed points-I [J]. Indian Journal of Pure and Applied Mathematics, 1999,30(8):827-837.
[13] 王尚志,李伯渝,高智民.膨胀映射及其不动点定理[J].数学进展,1982,11(2):149-153.
相似文献/References:
[1]沈京虎,朴勇杰.D -度量空间上一族拟收缩自映射的唯一公共不动点[J].延边大学学报(自然科学版),2014,40(01):8.
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[2]许明星,黄鑫,朴勇杰*.具有系数s的b -D-度量空间上4个映射的唯一公共不动点[J].延边大学学报(自然科学版),2016,42(02):95.
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备注/Memo
收稿日期: 2014-12-23 基金项目: 国家自然科学基金资助项目(11361064)*通信作者: 朴勇杰(1962—),男,理学博士,教授,研究方向为非线性分析和不动点理论.