Some common fixed point results for rational type contraction mappings in partially ordered metric spaces

Sumit Chandok

Mathematica Bohemica (2013)

  • Volume: 138, Issue: 4, page 407-413
  • ISSN: 0862-7959

Abstract

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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).

How to cite

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Chandok, Sumit. "Some common fixed point results for rational type contraction mappings in partially ordered metric spaces." Mathematica Bohemica 138.4 (2013): 407-413. <http://eudml.org/doc/260597>.

@article{Chandok2013,
abstract = {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).},
author = {Chandok, Sumit},
journal = {Mathematica Bohemica},
keywords = {common fixed point; rational type contraction mapping; compatible mapping; weakly compatible mapping; ordered metric space; common fixed point; rational type contraction mapping; weakly compatible mapping; ordered metric space},
language = {eng},
number = {4},
pages = {407-413},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some common fixed point results for rational type contraction mappings in partially ordered metric spaces},
url = {http://eudml.org/doc/260597},
volume = {138},
year = {2013},
}

TY - JOUR
AU - Chandok, Sumit
TI - Some common fixed point results for rational type contraction mappings in partially ordered metric spaces
JO - Mathematica Bohemica
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 138
IS - 4
SP - 407
EP - 413
AB - 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).
LA - eng
KW - common fixed point; rational type contraction mapping; compatible mapping; weakly compatible mapping; ordered metric space; common fixed point; rational type contraction mapping; weakly compatible mapping; ordered metric space
UR - http://eudml.org/doc/260597
ER -

References

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  1. Agarwal, R. P., El-Gebeily, M. A., O'Regan, D., 10.1080/00036810701556151, Appl. Anal. 87 (2008), 109-116. (2008) Zbl1140.47042MR2381749DOI10.1080/00036810701556151
  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. (2006) Zbl1106.47047MR2245511
  3. Branciari, A., 10.1155/S0161171202007524, Int. J. Math. Math. Sci. 29 (2002), 531-536. (2002) Zbl0993.54040MR1900344DOI10.1155/S0161171202007524
  4. Chandok, S., Some common fixed point theorems for generalized f -weakly contractive mappings, J. Appl. Math. Inform. 29 (2011), 257-265. (2011) Zbl1234.54053MR2798587
  5. Chandok, S., 10.1016/j.camwa.2011.09.009, Comput. Math. Appl. 62 (2011), 3692-3699. (2011) Zbl1236.65062MR2852091DOI10.1016/j.camwa.2011.09.009
  6. Chandok, S., Common fixed points for generalized nonlinear contractive mappings in metric spaces, Mat. Vesnik 65 (2013), 29-34. (2013) MR3001747
  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. (2013) MR3069265
  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. (2010) Zbl1203.54041MR2726609
  9. Jaggi, D. S., Some unique fixed point theorems, Indian J. Pure Appl. Math. 8 (1977), 223-230. (1977) Zbl0379.54015MR0500887
  10. Nieto, J. J., Rodríguez-López, R., 10.1007/s11083-005-9018-5, Order 22 (2005), 223-239. (2005) Zbl1095.47013MR2212687DOI10.1007/s11083-005-9018-5
  11. Ran, A. C. M., Reurings, M. C. B., 10.1090/S0002-9939-03-07220-4, Proc. Am. Math. Soc. 132 (2004), 1435-1443. (2004) Zbl1060.47056MR2053350DOI10.1090/S0002-9939-03-07220-4

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