Some results of common fixed point for four self-maps satisfying a new \(\Psi\)-contractive condition in partial metric spaces
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Authors
Hui-hui Zheng
- Institute of Applied Mathematics and Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China.
Feng Gu
- Institute of Applied Mathematics and Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China.
Abstract
In this paper, we prove some common fixed point theorems for two pairs of weakly compatible self-
maps satisfying a new \(\psi\) -contractive condition in the framework of a partial metric space. We also provide
illustrative examples in support of our new results. The results obtained in this paper differ from the recent
relative results in literature.
Share and Cite
ISRP Style
Hui-hui Zheng, Feng Gu, Some results of common fixed point for four self-maps satisfying a new \(\Psi\)-contractive condition in partial metric spaces, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 2258--2272
AMA Style
Zheng Hui-hui, Gu Feng, Some results of common fixed point for four self-maps satisfying a new \(\Psi\)-contractive condition in partial metric spaces. J. Nonlinear Sci. Appl. (2016); 9(5):2258--2272
Chicago/Turabian Style
Zheng, Hui-hui, Gu, Feng. "Some results of common fixed point for four self-maps satisfying a new \(\Psi\)-contractive condition in partial metric spaces." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 2258--2272
Keywords
- \(\psi\) -type contractive mapping
- common fixed point
- coincidence point
- partial metric space
- weakly compatible mappings.
MSC
References
-
[1]
T. Abdeljawad, Fixed points and generalized weakly contractive mappings in partial metric spaces, Math. Comput. Modelling, 54 (2011), 2923-2927.
-
[2]
T. Abdeljawad, E. Karapinar, K. Taş , Existence and uniqueness of a common fixed point on partial metric spaces , Appl. Math. Lett., 24 (2011), 1900-1904.
-
[3]
T. Abdeljawad, E. Karapinar, K. Taş, A generalized contraction principle with control functions on partial metric spaces, Comput. Math. Appl., 63 (2012), 716-719.
-
[4]
M. Akram, E. W. Shamaila, Fixed point results in partial metric spaces using generalized weak contractive conditions, J. Math. Comput. Sci., 12 (2014), 85-98.
-
[5]
I. Altun, Ö Acar, Fixed point theorems for weak contractions in the sense of Berinde on partial metric spaces, Topology Appl., 159 (2012), 2642-2648.
-
[6]
H. Aydi, Some fixed point results in ordered partial metric spaces, J. Nonlinear Sci. Appl., 4 (2011), 210-217.
-
[7]
H. Aydi , Fixed point theorems for generalized weakly contractive in ordered partial metric spaces, J. Nonlinear Anal. Optim. Theory Appl., 2 (2011), 269-284.
-
[8]
H. Aydi, M. Abbas, C. Vetroc , Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces , Topology Appl., 159 (2012), 3234-3242.
-
[9]
C. H. Chen, C. M. Chen, Fixed point results for Meir-Keeler-type \(\phi-\alpha\)-contractions on partial metric spaces, J. Inequal. Appl., 2013 (2013), 9 pages.
-
[10]
C. Chen, C. Zhu, Fixed point theorems for weakly C-contractive mappings in partial metric spaces , Fixed Point Theory Appl., 2013 (2013), 16 pages.
-
[11]
K. P. Chi, E. Karapinar, T. D. Thanha, A generalized contraction principle in partial metric spaces, Math. Comput. Modelling, 55 (2012), 1673-1681.
-
[12]
L. Ćirić, B. Samet, H. Aydi, C. Vetro, Common fixed point results of generalized contractions on partial metric spaces and application, Appl. Math. Comput., 218 (2011), 2398-2406.
-
[13]
A. Erduran, Z. Kadelburg, H. K. Nashine, C. Vetro , A fixed point theorem for (\(\varphi,L\))-weak contraction mappings on a partial metric space , J. Nonlinear Sci. Appl., 7 (2014), 196-204.
-
[14]
D. Ilić, V. Pavlović, V. Rakočević, Some new extensions of Banach's contraction principle to partial metric space, Appl. Math. Lett., 24 (2011), 1326-1330.
-
[15]
D. Ilić, V. Pavlović, V. Rakočević, Extensions of the Zamfirescu theorem to partial metric spaces , Math. Comput. Modelling, 55 (2012), 801-809.
-
[16]
A. Kaewcharoen, T. Yuying, Unique common fixed point theorems on partial metric spaces , J. Nonlinear Sci. Appl., 7 (2014), 90-101.
-
[17]
E. Karapinar, Ćirić types nonunique fixed point theorems on partial metric spaces, J. Nonlinear Sci. Appl., 5 (2012), 74-83.
-
[18]
E. Karapinar, I. Erhan, Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett., 24 (2011), 1894-1899.
-
[19]
E. Karapinar, I. M. Erhan, A. Y. Ulus, Fixed point theorem for cyclic maps on partial metric spaces, Appl. Math. Inf. Sci., 6 (2012), 239-244.
-
[20]
S. G. Matthews, Partial metric topology, In General Topology and Its Applications, Proc. 8th Summer Conf., Queen's College (1992). Annals New York Acad. Sci., 728 (1994), 183-197.
-
[21]
H. K. Nashine, Z. Kadelburg, S. Radenović, Common fixed point theorems for weakly isotone increasing mappings in ordered partial metric spaces, Math. Comput. Modelling, 57 (2013), 2355-2365.
-
[22]
T. Nazir, M. Abbas, Common fixed points of two pairs of mappings satisfying (E.A)-property in partial metric spaces, J. Inequal. Appl., 2014 (2014), 12 pages.
-
[23]
S. Oltra, O. Valero, Banach's fixed point theorem for partial metric spaces, Rend. Ist. Mat. Univ. Trieste, 36 (2004), 17-26.
-
[24]
V. L. Rosa, P. Vetro, Fixed points for Geraghty-contractions in partial metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 1-10.
-
[25]
W. Shatanawi, H. K. Nashine, A generalization of Banach's contraction principle for nonlinear contraction in a partial metric space , J. Nonlinear Sci. Appl., 5 (2012), 37-43.
-
[26]
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.
-
[27]
F. Vetro, S. Radenovic , Nonlinear w-quasi-contractions of Oirić-type in partial metric spaces , Appl. Math. Comput., 219 (2012), 1594-1600.
-
[28]
C. Vetro, F. Vetro, Common fixed points of mappings satisfying implicit relations in partial metric spaces , J. Nonlinear Sci. Appl., 6 (2013), 152-161.