Contraction mapping principle in partially ordered quasi metric space concerning to wdistances

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Authors
Rahma Zuhra
 School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, UKM, 43600 Bangi, Malaysia.
 Department of Mathematics, Faculty of Mathematics and Natural Sciences, Syiah Kuala University, 23111 Banda Aceh, Indonesia.
Mohd Salmi Md Noorani
 School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, UKM, 43600 Bangi, Malaysia.
Fawzia Shaddad
 Department of Mathematics, Sana’a University, Yemen.
Abstract
The fixed point theorems in various contraction mappings have been provided by many researchers. Some of them used
certain functions in mapping to guarantee the existence of fixed point. The purpose of this paper is to present some fixed
point result on contraction mapping in partially ordered quasimetric space that applying a wdistance. The generalized altering
distance function on the mapping plays a role in theorems. The results extend some wellknown results in the references. We
also improve these new results to the common fixed point.
Share and Cite
ISRP Style
Rahma Zuhra, Mohd Salmi Md Noorani, Fawzia Shaddad, Contraction mapping principle in partially ordered quasi metric space concerning to wdistances, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 2, 699712
AMA Style
Zuhra Rahma, Noorani Mohd Salmi Md, Shaddad Fawzia, Contraction mapping principle in partially ordered quasi metric space concerning to wdistances. J. Nonlinear Sci. Appl. (2017); 10(2):699712
Chicago/Turabian Style
Zuhra, Rahma, Noorani, Mohd Salmi Md, Shaddad, Fawzia. "Contraction mapping principle in partially ordered quasi metric space concerning to wdistances." Journal of Nonlinear Sciences and Applications, 10, no. 2 (2017): 699712
Keywords
 Fixed point
 wdistance
 a generalized altering distance function
 common fixed point.
MSC
References

[1]
M. Abbas, M. A. Khan, Common fixed point theorem of two mappings satisfying a generalized weak contractive condition, Int. J. Math. Math. Sci., 2009 (2009), 9 pages.

[2]
R. P. Agarwal, M. A. ElGebeily, D. O’Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., 87 (2008), 109–116.

[3]
C. Alegre, J. Marín, S. Romaguera, A fixed point theorem for generalized contractions involving wdistances on complete quasimetric spaces, Fixed Point Theory Appl., 2014 (2014), 8 pages.

[4]
L. Ćirić, R. P. Agarwal, B. Samet, Mixed monotonegeneralized contractions in partially ordered probabilistic metric spaces, Fixed Point Theory Appl., 2011 (2011), 13 pages.

[5]
L. Ćirić, N. Cakić, M. Rajović, J. S. Ume, Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory Appl., 2008 (2008), 11 pages.

[6]
P. N. Dutta, B. Choudhury, A generalisation of contraction principle in metric spaces, Fixed Point Theory Appl., 2008 (2008), 8 pages.

[7]
M. Eshaghi Gordji, H. Baghani, G. H. Kim, A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Discrete Dyn. Nat. Soc., 2012 (2012), 8 pages.

[8]
L. Gholizadeh, R. Saadati, W. Shatanawi, S. M. Vaezpour, Contractive mapping in generalized, ordered metric spaces with application in integral equations, Math. Probl. Eng., 2011 (2011), 14 pages.

[9]
R. H. Haghi, S. Rezapour, N. Shahzad, Some fixed point generalizations are not real generalizations, Nonlinear Anal., 74 (2011), 1799–1803.

[10]
J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations,/ Nonlinear Anal.,/ 72 (2010), 1188–1197., Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal., 72 (2010), 1188–1197.

[11]
D. Ilić, V. Rakočević, Common fixed points for maps on metric space with wdistance, Appl. Math. Comput., 199 (2008), 599–610.

[12]
M. Imdad, F. Rouzkard , Fixed point theorems in ordered metric spaces via wdistances, Fixed Point Theory Appl., 2012 (2012), 17 pages.

[13]
G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly, 83 (1976), 261–263.

[14]
O. Kada, T. Suzuki, W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japon., 44 (1996), 381–391.

[15]
M. S. Khan, M. Swaleh, S. Sessa, Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc., 30 (1984), 1–9.

[16]
A. Latif, S. A. AlMezel, Fixed point results in quasimetric spaces, Fixed Point Theory Appl., 2011 (2011), 8 pages.

[17]
S. H. Park, On generalizations of the Ekelandtype variational principles, Nonlinear Anal., 39 (2000), 881–889.

[18]
B. E. Rhoades, Some theorems on weakly contractive maps, Proceedings of the Third World Congress of Nonlinear Analysts, Part 4, Catania, (2000). Nonlinear Anal., 47 (2001), 2683–2693.

[19]
B. E. Rhoades, H. K. Pathak, S. N. Mishra, Some weakly contractive mapping theorems in partially ordered spaces and applications, Demonstratio Math., 45 (2012), 621–636.

[20]
F. Rouzkard, M. Imdad, D. Gopal , Some existence and uniqueness theorems on ordered metric spaces via generalized distances, Fixed Point Theory Appl., 2013 (2013), 20 pages.

[21]
R. Saadati, S. M. Vaezpoura, P. Vetro, B. E. Rhoades, Fixed point theorems in generalized partially ordered Gmetric spaces, Math. Comput. Modelling, 52 (2010), 797–801.

[22]
F. Shaddad, M. S. M. Noorani, S. M. Alsulami, H. Akhadkulov, Coupled point results in partially ordered metric spaces without compatibility, Fixed Point Theory Appl., 2014 (2014 ), 18 pages.

[23]
W. A. Shatanawi, K. K. Abodaye, A. Bataihah, Fixed point theorem through \(\Omega\)Distance of Suzuki type contraction condition, Gazi Univ. J. Sci., 29 (2016), 129–133.

[24]
W. Shatanawi, A. Bataihah, A. Pitea, Fixed and common fixed point results for cyclic mappings of \(\Omega\)distance, J. Nonlinear Sci. Appl., 9 (2016), 727–735.

[25]
W. Shatanawi, A. Pitea, Fixed and coupled fixed point theorems of \(\Omega\)distance for nonlinear contraction, Fixed Point Theory Appl., 2013 (2013 ), 16 pages.

[26]
W. Shatanawi, A. Pitea, \(\Omega\)distance and coupled fixed point in Gmetric spaces, Fixed Point Theory Appl.,, 2013 (2013 ), 15 pages.

[27]
W. Shatanawi, M. Postolache, Coincidence and fixed point results for generalized weak contractions in the sense of Berinde on partial metric spaces, Fixed Point Theory Appl., 2013 (2013 ), 17 pages.

[28]
Y.F. Su, Contraction mapping principle with generalized altering distance function in ordered metric spaces and applications to ordinary differential equations, Fixed Point Theory Appl., 2014 (2014 ), 15 pages.

[29]
F.F. Yan, Y.F. Su, Q.S. Feng, A new contraction mapping principle in partially ordered metric spaces and applications to ordinary differential equations, Fixed Point Theory Appl., 2012 (2012 ), 13 pages.