Journal of Applied Mathematics

• J. Appl. Math.
• Volume 2013, Special Issue (2013), Article ID 352927, 10 pages.

Some Common Coupled Fixed Point Results for Generalized Contraction in Complex-Valued Metric Spaces

Abstract

We introduce and study the notion of common coupled fixed points for a pair of mappings in complex valued metric space and demonstrate the existence and uniqueness of the common coupled fixed points in a complete complex-valued metric space in view of diverse contractive conditions. In addition, our investigations are well supported by nontrivial examples.

Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2013), Article ID 352927, 10 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394807742

Digital Object Identifier
doi:10.1155/2013/352927

Mathematical Reviews number (MathSciNet)
MR3070008

Zentralblatt MATH identifier
1271.54083

Citation

Kutbi, Marwan Amin; Azam, Akbar; Ahmad, Jamshaid; Di Bari, Cristina. Some Common Coupled Fixed Point Results for Generalized Contraction in Complex-Valued Metric Spaces. J. Appl. Math. 2013, Special Issue (2013), Article ID 352927, 10 pages. doi:10.1155/2013/352927. https://projecteuclid.org/euclid.jam/1394807742

References

• A. Azam, B. Fisher, and M. Khan, “Common fixed point theorems in complex valued metric spaces,” Numerical Functional Analysis and Optimization, vol. 32, no. 3, pp. 243–253, 2011.
• J. Ahmad, M. Arshad, and C. Vetro, “On a theorem of Khan in a generalized metric space,” International Journal of Analysis, vol. 2013, Article ID 852727, 6 pages, 2013.
• M. Arshad, A. Shoaib, and I. Beg, “Fixed point of a pair of contractive dominated mappings on a closed ball in an ordered complete dislocated metric space,” Fixed Point Theory and Applications, vol. 2013, article 115, 2013.
• M. Arshad, J. Ahmad, and E. Karapinar, “Some common fixed point results in rectangular metric spaces,” International Journal of Analysis, vol. 2013, Article ID 307234, 7 pages, 2013.
• M. Arshad and J. Ahmad, “On multivalued contractions in cone metric spaces without normality,” The Scientific World Journal. In press.
• M. Arshad, E. Karapinar, and J. Ahmad, “Some unique fixed point theorem for rational contractions in partially ordered metric spaces,” Journal of Inequalities and Applications, vol. 2013, article 248, 2013.
• H. Aydi, E. Karap\inar, and W. Shatanawi, “Tripled fixed point results in generalized metric spaces,” Journal of Applied Mathematics, vol. 2012, Article ID 314279, 10 pages, 2012.
• H. Aydi, E. Karap\inar, and C. Vetro, “Meir-Keeler type contractions for tripled fixed points,” Acta Mathematica Scientia B, vol. 32, no. 6, pp. 2119–2130, 2012.
• H. Aydi, B. Samet, and C. Vetro, “Coupled fixed point results in cone metric spaces for $\widetilde{\omega }$-compatible mappings,” Fixed Point Theory and Applications, vol. 2011, article 27, 15 pages, 2011.
• A. Azam and M. Arshad, “Common fixed points of generalized contractive maps in cone metric spaces,” Iranian Mathematical Society, vol. 35, no. 2, pp. 255–264, 2009.
• C. di Bari and P. Vetro, “$\varphi$-pairs and common fixed points in cone metric spaces,” Rendiconti del Circolo Matematico di Palermo Series 2, vol. 57, no. 2, pp. 279–285, 2008.
• C. di Bari and P. Vetro, “Weakly $\varphi$-pairs and common fixed points in cone metric spaces,” Rendiconti del Circolo Matematico di Palermo Series 2, vol. 58, no. 1, pp. 125–132, 2009.
• S. Bhatt, S. Chaukiyal, and R. C. Dimri, “Common fixed point of mappings satisfying rational inequality in complex valued metric space,” International Journal of Pure and Applied Mathematics, vol. 73, no. 2, pp. 159–164, 2011.
• N. Hussain, M. A. Khamsi, and A. Latif, “Banach operator pairs and common fixed points in hyperconvex metric spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 17, pp. 5956–5961, 2011.
• M. A. Kutbi, J. Ahmad, N. Hussain, and M. Arshad, “Common fixed point results for mappingsčommentComment on ref. [20?]: Please update the information of these references [4,20?], if possible. with rational expressions,” Abstract and Applied Analysis. In press.
• E. Karap\inar, “Some nonunique fixed point theorems of Ćirić type on cone metric spaces,” Abstract and Applied Analysis, vol. 2010, Article ID 123094, 14 pages, 2010.
• E. Karap\inar, “Couple fixed point theorems for nonlinear contractions in cone metric spaces,” Computers & Mathematics with Applications, vol. 59, no. 12, pp. 3656–3668, 2010.
• C. Mongkolkeha, W. Sintunavarat, and P. Kumam, “Fixed point theorems for contraction mappings in modular metric spaces,” Fixed Point Theory and Applications, vol. 2011, article 93, 2011.
• F. Rouzkard and M. Imdad, “Some common fixed point theorems on complex valued metric spaces,” Computers & Mathematics with Applications, vol. 64, no. 6, pp. 1866–1874, 2012.
• W. Sintunavarat and P. Kumam, “Generalized common fixed point theorems in complex valued metric spaces and applications,” Journal of Inequalities and Applications, vol. 2012, article 84, 2012.
• W. Sintunavarat, Y. J. Cho, and P. Kumam, “Urysohn integral equations approach by common fixed points in complex valued metric spaces,” Advances in Difference Equations, vol. 2013, article 49, 2013.
• W. Sintunavarat and P. Kumam, “Weak condition for generalized multi-valued $(f,\alpha ,\beta )$-weak contraction mappings,” Applied Mathematics Letters, vol. 24, no. 4, pp. 460–465, 2011.
• W. Sintunavarat, Y. J. Cho, and P. Kumam, “Common fixed point theorems for $c$-distance in ordered cone metric spaces,” Computers & Mathematics with Applications, vol. 62, no. 4, pp. 1969–1978, 2011.
• W. Sintunavarat and P. Kumam, “Common fixed point theorems for generalized $JH$-operator classes and invariant approximations,” Journal of Inequalities and Applications, vol. 2011, article 67, 2011.
• W. Sintunavarat and P. Kumam, “Common fixed points of $f$-weak contractors in cone metric spaces,” Bulletin of the Iranian Mathematical Society, vol. 38, no. 2, pp. 293–303, 2012.
• N. Tahat, H. Aydi, E. Karapinar, and W. Shatanawi, “Common fixed points for single-valued and multi-valued maps satisfying a generalized contraction in G-metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 48, 2012.
• T. Gnana Bhaskar and V. Lakshmikantham, “Fixed point theorems in partially ordered metric spaces and applications,” Nonlinear Analysis: Theory, Methods & Applications, vol. 65, no. 7, pp. 1379–1393, 2006.
• B. Samet, E. Karapinar, H. Aydi, and V. Cojbasic, “Discussion on some coupled fixed point theorems,” Fixed Point Theory and Applications, vol. 2013, article 50, 2013.
• B. Samet and C. Vetro, “Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 12, pp. 4260–4268, 2011.