Some fixed point theorems for contractive mappings of integral type
-
2240
Downloads
-
3647
Views
Authors
Zeqing Liu
- Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, People’s Republic of China.
Yuqing Wang
- Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, People’s Republic of China.
Shin Min Kang
- Department of Mathematics and the RINS, Gyeongsang National University, Jinju 52828, Korea.
- Center for General Education, , China Medical University, Taichung 40402, Taiwan.
Young Chel Kwun
- Department of Mathematics, Dong-A University, Busan 49315, Korea.
Abstract
Four fixed point theorems for mappings satisfying contractive conditions of integral type in complete metric spaces are
proved. The results presented in this paper extend and improve a few results existing in literature. Two examples involving the
contractive mappings of integral type are constructed.
Share and Cite
ISRP Style
Zeqing Liu, Yuqing Wang, Shin Min Kang, Young Chel Kwun, Some fixed point theorems for contractive mappings of integral type, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 7, 3566--3580
AMA Style
Liu Zeqing, Wang Yuqing, Kang Shin Min, Kwun Young Chel, Some fixed point theorems for contractive mappings of integral type. J. Nonlinear Sci. Appl. (2017); 10(7):3566--3580
Chicago/Turabian Style
Liu, Zeqing, Wang, Yuqing, Kang, Shin Min, Kwun, Young Chel. "Some fixed point theorems for contractive mappings of integral type." Journal of Nonlinear Sciences and Applications, 10, no. 7 (2017): 3566--3580
Keywords
- Contractive mappings of integral type
- fixed point
- complete metric space.
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]
H. H. Alsulami, E. Karapınar, D. O’Regan, P. Shahi, Fixed points of generalized contractive mappings of integral type, Fixed Point Theory Appl., 24 pages. (2014)
-
[3]
A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 29 (2002), 531–536.
-
[4]
D. Dey, A. Ganguly, M. Saha, Fixed point theorems for mappings under general contractive condition of integral type, Bull. Math. Anal. Appl., 3 (2011), 27–34.
-
[5]
P. N. Dutta, B. S. Choudhury, A generalisation of contraction principle in metric spaces, Fixed Point Theory Appl., 2008 (2008), 8 pages.
-
[6]
R. George, R. Rajagopalan, Common fixed point results for \(\psi-\phi\) contractions in rectangular metric spaces, Bull. Math. Anal. Appl., 5 (2013), 44–52.
-
[7]
V. Gupta, N. Mani, A common fixed point theorem for two weakly compatible mappings satisfying a new contractive condition of integral type, Math. Theory Modeling, 1 (2011), 6 pages.
-
[8]
V. Gupta, N. Mani, Common fixed point for two self-maps satisfying a generalized \(^\psi\int_\phi\) weakly contractive condition of integral type, Int. J. Nonlinear Sci., 16 (2013), 64–71.
-
[9]
V. Gupta, N. Mani, A. K. Tripathi, A fixed point theorem satisfying a generalized weak contractive condition of integral type, Int. J. Math. Anal. (Ruse), 6 (2012), 1883–1889.
-
[10]
V. R. Hosseini, Common fixed point for generalized (\(\phi,\psi\))-weak contractions contractions mappings condition of integral type, Int. J. Math. Anal., 4 (2010), 1535–1543.
-
[11]
E. Karapınar, P. Shahi, K. Tas, Generalized \(\alpha-\psi\)-contractive type mappings of integral type and related fixed point theorems, J. Inequal. Appl., 2014 (2014), 18 pages.
-
[12]
M. A. Kutbi, M. Imdad, S. Chauhan, W. Sintunavarat, Some integral type fixed point theorems for non-self-mappings satisfying generalized (\(\psi,\phi\))-weak contractive conditions in symmetric spaces, Abstr. Appl. Anal., 2014 (2014), 11 pages.
-
[13]
Z.-Q. Liu, J.-L. Li, S. M. Kang, Fixed point theorems of contractive mappings of integral type, Fixed Point Theory Appl., 2013 (2013), 17 pages.
-
[14]
Z.-Q. Liu, X. Li, S. M. Kang, S. Y. Cho, Fixed point theorems for mappings satisfying contractive conditions of integral type and applications, Fixed Point Theory Appl., 2011 (2011), 18 pages.
-
[15]
Z.-Q. Liu, H. Wu, J. S. Ume, S. M. Kang, Some fixed point theorems for mappings satisfying contractive conditions of integral type, Fixed Point Theory Appl., 2014 (2014), 14 pages.
-
[16]
N. V. Luong, N. X. Thuan, A fixed point theorem for \(\psi_{\int \phi}\)-weakly contractive mapping in metric spaces, Int. J. Math. Appl., 4 (2010), 233–242.
-
[17]
C. Mongkolkeha, P. Kumam, Fixed point and common fixed point theorems for generalized weak contraction mappings of integral type in modular spaces, Int. J. Math. Math. Sci., 2011 (2011), 12 pages.
-
[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, Two fixed-point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 2003 (2003), 4007–4013.