Coincidence point results via generalized \((\psi,\phi)\)-weak contractions in partial ordered \(b\)-metric spaces with application
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Authors
Muhammad Sarwar
- Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan.
Noor Jamal
- Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan.
Yongjin Li
- Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, P. R. China.
Abstract
In this manuscript, some coincidence point and fixed point results via generalized \((\psi,\phi)\)-weak contractive condition are
established. The presented work explicitly generalize some recent results from the existing literature in the setting of partial
order b-metric spaces. An example is provided to show the authenticity of the derived results.
Share and Cite
ISRP Style
Muhammad Sarwar, Noor Jamal, Yongjin Li, Coincidence point results via generalized \((\psi,\phi)\)-weak contractions in partial ordered \(b\)-metric spaces with application, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 7, 3719--3731
AMA Style
Sarwar Muhammad, Jamal Noor, Li Yongjin, Coincidence point results via generalized \((\psi,\phi)\)-weak contractions in partial ordered \(b\)-metric spaces with application. J. Nonlinear Sci. Appl. (2017); 10(7):3719--3731
Chicago/Turabian Style
Sarwar, Muhammad, Jamal, Noor, Li, Yongjin. "Coincidence point results via generalized \((\psi,\phi)\)-weak contractions in partial ordered \(b\)-metric spaces with application." Journal of Nonlinear Sciences and Applications, 10, no. 7 (2017): 3719--3731
Keywords
- coincidence point
- weak compatible mapping
- increasing pairs of maps
- Generalized \((\psi،\phi)\)-weak contraction
- partial ordered complete b-metric spaces.
MSC
References
-
[1]
M. Abbas, D. Đorić, Common fixed point for generalized \((\psi,\phi)\)-weak contractions, Math. Un. of Nis. Serbia., 10 (2010), 1–10.
-
[2]
M. Abbas, T. Nazir, S. Radenović, Common fixed points of four maps in partially ordered metric spaces, Appl. Math. Lett., 24 (2011), 1520–1526.
-
[3]
A. Aghajani, M. Abbas, J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 64 (2014), 941–960.
-
[4]
R. Allahyari, R. Arab, A. Shole Haghighi, A generalization on weak contractions in partially ordered b-metric spaces and its application to quadratic integral equations, J. Inequal. Appl., 2014 (2014), 15 pages.
-
[5]
I. Altun, H. Simsek, Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl., 2010 (2010), 17 pages.
-
[6]
S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), 263–276.
-
[7]
D. Dorić, Common fixed point for generalized \((\psi,\phi)\)-weak contractions, Appl. Math. Lett., 22 (2009), 1896–1900.
-
[8]
P. N. Dutta, B. S. Choudhury, A generalisation of contraction principle in metric spaces, Fixed Point Theory Appl., 18 (2008), 8 pages.
-
[9]
J. Esmaily, S. M. Vaezpour, B. E. Rhoades, Coincidence point theorem for generalized weakly contractions in ordered metric spaces, Appl. Math. Comput., 219 (2012), 1536–1548.
-
[10]
M. Jovanović, Z. Kadelburg, S. Radenović, Common fixed point results in metric-type spaces, Fixed Point Theory Appl., 2010 (2010), 15 pages.
-
[11]
G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci., 4 (1986), 771–779.
-
[12]
G. Jungck, Common fixed points for noncontinuous nonself maps on nonmetric spaces, Far East J. Math. Sci., 4 (1996), 199–215.
-
[13]
P. P. Murthy, K. Tas, U. Devi Patel, Common fixed point theorems for generalized \((\phi,\psi)\)-weak contraction condition in complete metric spaces, J. Inequal. Appl., 2015 (2015), 14 pages.
-
[14]
H. K. Nashine, B. Samet, Fixed point results for mappings satisfying \((\psi,\phi)\)-weakly contractive condition in partially ordered metric spaces, Nonlinear Anal., 74 (2011), 2201–2209.
-
[15]
S. Radenović, Z. Kadelburg, Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl., 60 (2010), 1776–1783.
-
[16]
A. C. M. Ran , M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435–1443.
-
[17]
K. P. R. Rao, I. Altun, K. R. K. Rao, N. Srinivasarao, A common fixed point theorem for four maps under \((\psi,\phi)\) contractive condition of integral type in ordered partial metric spaces, Math. Sci. Lett., 4 (2015), 25–31.
-
[18]
A. Razani, V. Parvaneh, M. Abbas, A common fixed point for generalized \((\psi,\phi)_{f,g}\)-weak contractions, Ukrainian Math. J., 63 (2012), 1756–1769.
-
[19]
J. R. Roshan, V. Parvaneh, I. Altun, Some coincidence point results in ordered b-metric spaces and applications in a system of integral equations, Appl. Math. Comput., 226 (2014), 725–737.
-
[20]
J. R. Roshan, V. Parvaneh, S. Radenović, M. Rajović, Some coincidence point results for generalized \((\psi,\varphi)\)-weakly contractions in ordered b-metric spaces, Fixed Point Theory Appl., 2015 (2015), 21 pages.
-
[21]
J. R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei,W. Shatanawi, Common fixed points of almost generalized \((\psi,\varphi)_s\)- contractive mappings in ordered b-metric spaces, Fixed Point Theory Appl., 2013 (2013), 23 pages.
-
[22]
W. Shatanawi, B. Samet, On \((\psi,\phi)\)-weakly contractive condition in partially ordered metric spaces, Comput. Math. Appl., 62 (2011), 3204–3214.