Common coupled fixed point results for contractive type conditions on $S$-metric spaces

Gurucharan Singh Saluja

Abstract


In this paper, we prove some common coupled fixed point theorems for contractive type conditions on $S$-metric spaces. We give some consequences of the main results. We also give an example to validate the result. The results of findings in this paper generalize, extend and unify several previous results in the existing literature.

Full Text:

PDF

References


bibitem{AR09} M. Abbas and B. E. Rhoades, Common fixed point results for non-commuting mappings without continuity generalized metric spaces, Appl. Math. Computation {bf 215} (2009), 262-269.

bibitem{AKR10} M. Abbas, M. Ali Khan and S. Radenovi$acute{c}$, Common coupled fixed point theorems in cone metric spaces for $w$-compatible mappings, Appl. Math. Comput. {bf 217} (2010), 195-202.

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{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{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{DHR14} N. V. Dung, N. T. Hieu and S. Radojevi$acute{c}$, Fixed point theorems for $g$-monotone maps on partially ordered $S$-metric spaces, Filomat {bf 28(9)} (2014), 1885-1898.

bibitem{G13} A. Gupta, Cyclic contraction on $S$-metric space, Int. J. Anal. Appl. {bf 3(2)} (2013), 119-130.

bibitem{GL87} D. Guo and V. Lakshmikantham, Coupled fixed point of nonlinear operator with application, Nonlinear Anal. TMA., {bf 11} (1987), 623-632.

bibitem{HLD15} N. T. Hieu, N. T. Ly and N. V. Dung, A generalization of Ciric quasi-contractions for maps on $S$-metric spaces, Thai J. Math. {bf 13(2)} (2015), 369-380.

bibitem{J86} G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. {bf 9} (1986), 771-779.

bibitem{JR98} G. Jungck and B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. {bf 29} 1998), 227-238.

bibitem{KSGR16} J. K. Kim, S. Sedghi, A. Gholidahneh and M. M. Rezaee, Fixed point theorems in $S$-metric spaces, East Asian Math. J. {bf 32(5)} (2016), 677-684.

bibitem{LT11} N. V. Luong and N. X. Thuan, Coupled fixed points theorems for mixed monotone mappings and an application to integral equations, Comput. Math. Appl. {bf 62} (2011), 4238-4248.

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{OOA12} J. O. Olaleru, G. A. Okeke and H. Akewe, Coupled fixed point theorems for generalized $varphi$-mappings satisfying contractive condition of integral type on cone metric spaces, Int. J. Math. Model. Comput. {bf 2(2)} (2012), 87-98.

bibitem{OT17b} N. Y. $ddot{O}$zg$ddot{u}$r and N. Tas, Some new contractive mappings on $S$-metric spaces and their relationships with the mapping ${bf (S25)}$, Math. Sci. {bf 11(7)} (2017), 7-16.

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{SSA12} S. Sedghi, N. Shobe and A. Aliouche, A generalization of fixed point theorems in $S$-metric spaces, Mat. Vesnik {bf 64(3)} (2012), 258-266.

bibitem{SD14} S. Sedghi and N. V. Dung, Fixed point theorems on $S$-metric spaces, Mat. Vesnik {bf 66(1)} (2014), 113-124.

bibitem{SRDR16} S. Sedghi, M. M. Rezaee, T. Dosenovic and S. Radenovic, Common fixed point theorems for contractive mappings satisfying $Phi$-maps in $S$-metric spaces, Acta Univ. Sapientiae Math. {bf 8(2)} (2016), 298-311.

bibitem{SSSD18} S. Sedghi, N. Shobkolaei, M. Shahraki and T. Dosenovic, Common fixed point of four maps in $S$-metric space, Math. Sci. {bf 12} (2018), 137-143.


Refbacks

  • There are currently no refbacks.