Coupled fixed point results based on control function in complex partial metric spaces

Gurucharan Singh Saluja

Abstract


The purpose of this article is to establish some coupled fixed point results based on control function in the setting of complex partial metric spaces. Furthermore, we give some consequences of the established result. An example is given to support the result. The results of findings in this article extend and generalize several results from the existing literature. Specially, our results extend the corresponding results of {\it Aydi} \cite{A11}.

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bibitem{ACNR13} M. Abbas, V. Cojbaic Rajic, T. Nazir and S. Radenovic, Common fixed point of mappings satisfying rational inequalities in ordered complex valued generalized metric spaces, Afrika Mathematika (2013). doi:10.1007/s13370-013-0185-z.

bibitem{AAS14} J. Ahmad, A. Azam and S. Saejung, Common fixed point results for contractive mappings in complex valued metric spaces, Fixed Point Theory Appl. 2014(1), 67.

bibitem{AER17} A. H. Ansari, O. Ege and S. Radenovic, Some fixed point results on complex valued $G_{b}$-metric spaces, Revista de la Real Academia de Ciencias Exactas, Fsicasy Naturales. Series A, Matemiticas. doi: 10.1007/s13398-017-0391-x.

bibitem{A11} H. Aydi, Some coupled fixed point results on partial metric spaces, International J. Math. Math. Sci. 2011, Article ID 647091, 11 pages.

bibitem{AFK11} A. Azam, B. Fisher and M. Khan, Common fixed point theorems in complex valued metric spaces, Numer. Funct. Anal. Optim. {bf 3(3)} (2011), 243-253.

bibitem{B22} S. Banach, Sur les operation dans les ensembles abstraits et leur application aux equation integrals, Fund. Math.

{bf 3} (1922), 133-181.

bibitem{BL06} T. Gnana Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis: TMA, {bf 65(7)} (2006), 1379-1393.

bibitem{BCD11} S. Bhatt, S. Chaukiyal and R. C. Dimri, A common fixed point theorem for weakly compatible maps in complex valued metric spaces, Int. J. Math. Sci. Appl. {bf 1} (2011), 1385-1389.

bibitem{CK13} S. Chandok and D. Kumar, Some common fixed point results for rational type contraction mappings in complex valued metric spaces, J. Operators, 2013, Article ID 813707.

bibitem{CL09} L. Ciric and V. Lakshmikantham, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis: TMA, {bf 70(12)} (2009), 4341-4349.

bibitem{DM17} P. Dhivya and M. Marudai, Common fixed point theorems for mappings satisfying a contractive condition of rational expression on a ordered complex partial metric space, Cogent Math. (2017), 4:1389622.

bibitem{KR18} B. Khomdaram and Y. Rohen, Some common coupled fixed point theorems in $S_{b}$-metric spaces, Fasciculi Math. {bf 60} (2018), 79-92.

bibitem{KOL17} J. K. Kim, G. A. Okeke and W. H. Lim, Common coupled fixed point theorems for $w$-compatible mappings in partial metric spaces, Global J. Pure Appl. Math. {bf 13(2)} (2017), 519-536.

bibitem{K22} K. S. Kim, Coupled fixed point theorems under new coupled implicit relation in Hilbert spaces, Demonstratio Math. {bf 55} (2022), 81-89.

bibitem{KAAD13} M. A. Kutbi, A. Azam, J. Ahmad and C. Di Bari, Some common coupled fixed point results for generalized contraction in complex valued metric spaces, J. Appl. Math. (2013), Article ID 352927.

bibitem{N12} H. K. Nashine, Coupled common fixed point results in ordered $G$-metric spaces, J. Nonlinear Sci. Appl. {bf 1} (2012), 1-13.

bibitem{NKSS16} H. K. Nashine, J. K. Kim, A. K. Sharma and G. S. Saluja, Some coupled fixed point without mixed monotone mappings, Nonlinear Funct. Anal. Appl. {bf 21(2)} (2016), 235-247.

bibitem{RI12} F. Rouzkard and M. Imdad, Some common fixed point theorems on complex valued metric spaces, Computers and Mathematics with Applications (2012). doi:10.1016/j.camwa.2012.02.063.

bibitem{SMS09} F. Sabetghadam, H. P. Mashiha and A. H. Sanatpour, Some coupled fixed point theorems in cone metric spaces, Fixed Point Theory Appl. (2009), Article ID 125426, 8 pages.

bibitem{RK20} N. Seshagiri Rao and K. Kalyani, Coupled fixed point theorems in partially ordered metric spaces, Fasciculi Math. {bf 64} (2020), 77-89.

bibitem{SY} B. Samet and H. Yazidi, Coupled fixed point theorems for contraction involving rational expressions in partially ordered metric spaces, priprint, arXiv:1005.3142v1 [math GN].

bibitem{SG17} S. Sedghi and A. Gholidehneh, Coupled fixed point theorems in $S_{b}$-metric spaces, Nonlinear Funct. Anal. Appl. {bf 22(2)} (2017), 217-228.

bibitem{SSA12a} W. Shatanawi, B. Samet and M. Abbas, Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Math. Comput. Modell. {bf 55} (2012), Nos. 3-4, 680-687.

bibitem{SK12} W. Sintunavarat and P. Kumam, Generalized common fixed point theorems in complex valued metric spaces and applications, J. Inequ. Appl. 2012, {bf 2012:84}.

bibitem{SS12} K. Sittikul and S. Saejung, Some fixed point theorems in complex valued metric space, Fixed Point Theory Appl. 2012, 189.


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