| Title:
|
Some common fixed point results for rational type contraction mappings in partially ordered metric spaces (English) |
| Author:
|
Chandok, Sumit |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
138 |
| Issue:
|
4 |
| Year:
|
2013 |
| Pages:
|
407-413 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The purpose of this paper is to establish some common fixed point results for $f$-nondecreasing mappings which satisfy some nonlinear contractions of rational type in the framework of metric spaces endowed with a partial order. Also, as a consequence, a result of integral type for such class of mappings is obtained. The proved results generalize and extend some of the results of J. Harjani, B. Lopez, K. Sadarangani (2010) and D. S. Jaggi (1977). (English) |
| Keyword:
|
common fixed point |
| Keyword:
|
rational type contraction mapping |
| Keyword:
|
compatible mapping |
| Keyword:
|
weakly compatible mapping |
| Keyword:
|
ordered metric space |
| MSC:
|
37C25 |
| MSC:
|
41A50 |
| MSC:
|
46A19 |
| MSC:
|
46T99 |
| MSC:
|
47H10 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 06260041 |
| idMR:
|
MR3231095 |
| DOI:
|
10.21136/MB.2013.143513 |
| . |
| Date available:
|
2013-11-09T20:26:12Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143513 |
| . |
| Reference:
|
[1] Agarwal, R. P., El-Gebeily, M. A., O'Regan, D.: Generalized contractions in partially ordered metric spaces.Appl. Anal. 87 (2008), 109-116. Zbl 1140.47042, MR 2381749, 10.1080/00036810701556151 |
| Reference:
|
[2] Bhaskar, T. G., Lakshmikantham, V.: Fixed point theorems in partially ordered metric spaces and applications.Nonlinear Anal., Theory Methods Appl. 65 (2006), 1379-1393. Zbl 1106.47047, MR 2245511 |
| Reference:
|
[3] Branciari, A.: A fixed point theorem for mappings satisfying a general contractive condition of integral type.Int. J. Math. Math. Sci. 29 (2002), 531-536. Zbl 0993.54040, MR 1900344, 10.1155/S0161171202007524 |
| Reference:
|
[4] Chandok, S.: Some common fixed point theorems for generalized $f$-weakly contractive mappings.J. Appl. Math. Inform. 29 (2011), 257-265. Zbl 1234.54053, MR 2798587 |
| Reference:
|
[5] Chandok, S.: Some common fixed point theorems for generalized nonlinear contractive mappings.Comput. Math. Appl. 62 (2011), 3692-3699. Zbl 1236.65062, MR 2852091, 10.1016/j.camwa.2011.09.009 |
| Reference:
|
[6] Chandok, S.: Common fixed points for generalized nonlinear contractive mappings in metric spaces.Mat. Vesnik 65 (2013), 29-34. MR 3001747 |
| Reference:
|
[7] Chandok, S.: Some common fixed point results for generalized weak contractive mappings in partially ordered metric spaces.J. Nonlinear Anal. Opt. 4 (2013), 45-52. MR 3069265 |
| Reference:
|
[8] Harjani, J., Lopez, B., Sadarangani, K.: A fixed point theorem for mappings satisfying a contractive condition of rational type on a partially ordered metric space.Abstr. Appl. Anal. 2010, Article ID 190701 (2010), 8 p. Zbl 1203.54041, MR 2726609 |
| Reference:
|
[9] Jaggi, D. S.: Some unique fixed point theorems.Indian J. Pure Appl. Math. 8 (1977), 223-230. Zbl 0379.54015, MR 0500887 |
| Reference:
|
[10] Nieto, J. J., Rodríguez-López, R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations.Order 22 (2005), 223-239. Zbl 1095.47013, MR 2212687, 10.1007/s11083-005-9018-5 |
| Reference:
|
[11] Ran, A. C. M., Reurings, M. C. B.: A fixed point theorem in partially ordered sets and some applications to matrix equations.Proc. Am. Math. Soc. 132 (2004), 1435-1443. Zbl 1060.47056, MR 2053350, 10.1090/S0002-9939-03-07220-4 |
| . |
