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http://dx.doi.org/10.14403/jcms.2015.28.3.451

COMMON FIXED POINT THEOREMS FOR TWO MAPPINGS WITH ψ-ϕ-CONTRACTIVE OR EXPANSIVE TYPE CONDITIONS ON COMPLEX-VALUED METRIC SPACES  

JIN, HAI-LAN (Department of Mathematics Yanbian University)
PIAO, YONG-JIE (Department of Mathematics Yanbian University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.28, no.3, 2015 , pp. 451-463 More about this Journal
Abstract
A continuous and non-decreasing function ${\psi}$ and another continuous function ${\phi}$ with ${\phi}(z)=0{\Leftrightarrow}z=0$ defined on $\mathbb{C}^+=\{x+yi:x,y{\geq}0\}$ are introduced, the ${\psi}-{\phi}$-contractive or expansive type conditions are considered, and the existence theorems of common fixed points for two mappings defined on a complex valued metric space are obtained. Also, Banach contraction principle and a fixed point theorem for a I-expansive type mapping are given on complex valued metric spaces.
Keywords
complex valued metric space; ${\psi}-{\phi}$-contractive or expansive type condition; coincidence point; common fied point;
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1 A. Azam, B. Fisher, and M. Khan, Common fixed point theroems in complex valued metric spaces, Numer Funt Anal Optim. 32 (2011), no. 3, 243-353.   DOI   ScienceOn
2 C. D. Bari and P. Vetro P., ${\phi}$-pairs and common fixed points in cone metric spaces, Rendiconti del circlol Mathematico. 57 (2008), 279-285.
3 A. S. Cvetkovic, M. P. Stanic, S. Dimitrijevic and S. Simic, Common fixed point theorems for four mappings on cone metric type spaces, Fixed Point Theory and Applications (2011), Aeticle ID 589725, doi:10.1155/2011/589725.   DOI
4 L. G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), no. 2, 1468-1476.   DOI   ScienceOn
5 B. Ismat, A. Akbar, and A. Muhammad, Common fixed points for mapps on Topological vector space valued cone metric spaces, Inter. J. Math. and Math. Sci. 2009, doi:10.1155, ID.   DOI
6 Z. Kadelburg, P. P. Murthy, and S. Radenovic, Common fixed points for expansive mappings in cone metric spaces, Int. Journal of Math. Analysis 5 (27) (2011), 1309-1319.
7 Y. J. Piao, Fixed Point Theorems for III, s-III type Expansion Mappings On CMTS, Journal of Systems Science and Mathematical Sciences, 33(8) (2013), 976-984 (In Chinese).
8 Y. J. Piao, Common fixed points for two mappings with expansive properties in complex valued metric spaces, J. of the Chungcheong Mathematical Society 28 (2015), no. 1, 13-28.   DOI   ScienceOn
9 F. Rouzkard and M. Imdad, Some common fixed point theroems on complex valued metric spaces, Computers and Mathematics with Applications 64 (2012), 1866-1874.   DOI   ScienceOn
10 W. Shatanawi and F. Awawdeh, Some fixed and coincidence point theorems for expansive maps in cone metric spaces, Fixed point theory and Applications (2012), doi:10.1186/1687-1812-2012-19.   DOI   ScienceOn
11 M. P. Stanic, A. S. Cvetkovic, S. Simic, and S. Dimitrijevic, Common fixed point under contractive condition of ciric's type on cone metric type spaces, Fixed Point Theory and Applications (2012), doi:10.1186/1687-1812-2012-35.   DOI
12 W. Sintunavarat and P. Kumam, Generalized common fixed point theorems in complex valued metric spaces and application, J. of Inequalities and Applications 84 (2012), 12pages.
13 K. Sitthikul and S. Saejung, Some fixed point theorems in complex valued metric space, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2012-189.   DOI
14 B. Sandeep, C. Shruti, and R. C. Dimri, Common fixed point of mappings satisfying rational inequality in complex valued metric spaces, International Journal of Oure and Applied Mathematics 72 (2011), no. 2, 159-164.
15 B. Sandeep, C. Shruti, and R. C. Dimri, A common fixed point theorem for weakly compatible maps in complex valued metric spaces, Int. J of Mathematical Sciences and Applications 1 (3) (2011), 1385-1389.
16 I. Sahin and M. Telci. A theorem on common fixed points of expansion type mappings in cone metric spaces, An. St. Univ. Ovidius Constanta 18 (2010), no.1, 329-336.
17 J. S. Yan, Y. J. Piao, and H. Nan, Banach contractive principle and fixed point theorem for I-expansive mappings on complex valued metric spaces, Journal of Yunnan University(Natural Science Edition)(Chinese Series) 36 (2014), no. 2, 162-167.
18 S. Z. Wang, B. Y. Li, and A. M Gao, Expansive mappings and fixed point theorems, Advances in Mathematics(Chinese Series) 11 (1982), no. 2, 149-153.