Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


IMPACT FACTOR 2018: 0.490

CiteScore 2018: 0.47

SCImago Journal Rank (SJR) 2018: 0.279
Source Normalized Impact per Paper (SNIP) 2018: 0.627

Mathematical Citation Quotient (MCQ) 2017: 0.26

Online
ISSN
1337-2211
See all formats and pricing
More options …
Volume 64, Issue 4

Issues

Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces

Asadollah Aghajani / Mujahid Abbas
  • Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood road, Pretoria, 0002, South Africa
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Jamal Roshan
Published Online: 2014-09-07 | DOI: https://doi.org/10.2478/s12175-014-0250-6

Abstract

We prove some common fixed point results for four mappings satisfying generalized weak contractive condition in partially ordered complete b-metric spaces. Our results extend and improve several comparable results in the existing literature

MSC: Primary 47H10; Secondary 54H25

Keywords: common fixed point; compatible maps; b-metric space; partially ordered set

  • [1] ABBAS, M.— DORIĆ, D.: Common fixed point theorem for four mappings satisfying generalized weak contractive condition, Filomat 24 (2010), No. 2, 1–10. http://dx.doi.org/10.2298/FIL1002001ACrossrefGoogle Scholar

  • [2] ABBAS, M.— NAZIR, T.— RADENOVIĆ, S.: Common fixed points of four maps in partially ordered metric spaces, Appl. Math. Lett. 24 (2011), 1520–1526. http://dx.doi.org/10.1016/j.aml.2011.03.038CrossrefGoogle Scholar

  • [3] ALBER, YA. I.— GUERRE-DELABRIERE, S.: Principle of weakly contractive maps in Hilbert spaces. In: New Results in Operator Theory, I. (Gohberg, Yu, Lyubich, eds.). Advances and Applications, Vol. 98, Birkhäuser Verlag, Basel, 1997, pp. 7–22. http://dx.doi.org/10.1007/978-3-0348-8910-0_2CrossrefGoogle Scholar

  • [4] AMINI-HARANDI, A.— EMAMI, H.: A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal. 72 (2010), 2238–2242. http://dx.doi.org/10.1016/j.na.2009.10.023CrossrefWeb of ScienceGoogle Scholar

  • [5] BORICEANU, M.: Strict fixed point theorems for multivalued operators in b-metric spaces, Int. J. Mod. Math. 4 (2009), 285–301. Google Scholar

  • [6] BORICEANU, M.: Fixed point theory for multivalued generalized contraction on a set with two b-metrics, Stud. Univ. Babeş-Bolyai Math. LIV, (2009). Google Scholar

  • [7] BORICEANU, M.— BOTA, M.— PETRUSEL, A.: Multivalued fractals in b-metric spaces, Cent. Eur. J. Math. 8 (2010), 367–377. http://dx.doi.org/10.2478/s11533-010-0009-4CrossrefWeb of ScienceGoogle Scholar

  • [8] ĆIRIĈ, LJ.— CAKIĆ, N.— RAJOVIĆ, M.— UME, J. S.: Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory Appl. 2008, Article ID 131294, 11 pp. Google Scholar

  • [9] CZERWIK, S.: Nonlinear set-valued contraction mappings in b-metric spaces, Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia 46 (1998), 263–276. Google Scholar

  • [10] DORIĆ, D.: Common fixed point for generalized (ψ,φ)-weak contractions, Appl. Math. Lett. 22 (2009), 1896–1900. http://dx.doi.org/10.1016/j.aml.2009.08.001CrossrefGoogle Scholar

  • [11] DUTTA, P. N.— CHOUDHURY, B. S.: A generalization of contraction principle in metric spaces, Fixed Point Theory Appl. 2008, Article ID 406368, 8 pp. Web of ScienceGoogle Scholar

  • [12] HUSSAIN, N.— SHAH, M. H.: KKM mappings in cone b-metric spaces, Comput. Math. Appl. 62 (2011), 1677–1684. http://dx.doi.org/10.1016/j.camwa.2011.06.004CrossrefGoogle Scholar

  • [13] JACHYMSKI, J.: Equivalent conditions for generalized contractions on (ordered) metric spaces, Nonlinear Anal. 74 (2011), 768–774. http://dx.doi.org/10.1016/j.na.2010.09.025CrossrefGoogle Scholar

  • [14] JUNGCK, G.: Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986), 771–779. http://dx.doi.org/10.1155/S0161171286000935CrossrefGoogle Scholar

  • [15] KHAMSI, M. A.: Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl. 2010, Article ID 315398, 7 pp. Google Scholar

  • [16] KHAMSI, M. A.— HUSSAIN, N.: KKM mappings in metric type spaces, Nonlinear Anal. 73 (2010), 3123–3129. http://dx.doi.org/10.1016/j.na.2010.06.084CrossrefGoogle Scholar

  • [17] NASHINE, H. K.— SAMET, B.: Fixed point results for mappings satisfying (ψ,φ)-weakly contractive condition in partially ordered metric spaces, Nonlinear Anal. 74 (2011), 2201–2209. http://dx.doi.org/10.1016/j.na.2010.11.024CrossrefWeb of ScienceGoogle Scholar

  • [18] NIETO, J. J.— LOPEZ, R. R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005), 223–239. http://dx.doi.org/10.1007/s11083-005-9018-5CrossrefGoogle Scholar

  • [19] PACURAR, M.: Sequences of almost contractions and fixed points in b-metric spaces, An. Univ. Vest Timiş. Ser. Mat.—Inform. XLVIII (2010), 125–137. Google Scholar

  • [20] RADENOVIĆ, S.— KADELBURG, Z.: Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl. 60 (2010), 1776–1783. http://dx.doi.org/10.1016/j.camwa.2010.07.008CrossrefWeb of ScienceGoogle Scholar

  • [21] RAN, A. C. M.— REURINGS, M. C. B.: A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Amer.Math. Soc. 132 (2004), 1435–1443. http://dx.doi.org/10.1090/S0002-9939-03-07220-4CrossrefGoogle Scholar

  • [22] RHOADES, B. E.: Some theorems on weakly contractive maps, Nonlinear Anal. 47 (2001), 2683–2693. http://dx.doi.org/10.1016/S0362-546X(01)00388-1CrossrefGoogle Scholar

  • [23] SINGH, S. L.— PRASAD, B.: Some coincidence theorems and stability of iterative proceders, Comput. Math. Appl. 55 (2008), 2512–2520. http://dx.doi.org/10.1016/j.camwa.2007.10.026CrossrefWeb of ScienceGoogle Scholar

  • [24] ZHANG, Q.— SONG, Y.: Fixed point theory for generalized φ-weak contraction, Appl. Math. Lett. 22 (2009), 75–78. http://dx.doi.org/10.1016/j.aml.2008.02.007CrossrefGoogle Scholar

About the article

Published Online: 2014-09-07

Published in Print: 2014-08-01


Citation Information: Mathematica Slovaca, Volume 64, Issue 4, Pages 941–960, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-014-0250-6.

Export Citation

© 2014 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Suzana Aleksić, Huaping Huang, Zoran D. Mitrović, and Stojan Radenović
Journal of Fixed Point Theory and Applications, 2018, Volume 20, Number 4
[2]
Hassen Aydi, Radoje Banković, Ivan Mitrović, and Muhammad Nazam
Discrete Dynamics in Nature and Society, 2018, Volume 2018, Page 1
[3]
Kastriot Zoto and Ilir Vardhami
Journal of Function Spaces, 2018, Volume 2018, Page 1
[4]
Mian Bahadur Zada, Muhammad Sarwar, and Cemil Tunc
Journal of Fixed Point Theory and Applications, 2018, Volume 20, Number 1
[5]
Muhammad Nazam, Ma Zhenhua, Sami Ullah Khan, and Muhammad Arshad
Journal of Function Spaces, 2017, Volume 2017, Page 1
[8]
Noor Jamal, Muhammad Sarwar, and Mohammad Imdad
Transactions of A. Razmadze Mathematical Institute, 2017, Volume 171, Number 2, Page 182
[9]
Radu Miculescu and Alexandru Mihail
Journal of Fixed Point Theory and Applications, 2017, Volume 19, Number 2, Page 1525
[10]
Radu Miculescu and Alexandru Mihail
Journal of Fixed Point Theory and Applications, 2017
[11]
Nİhal Yilmaz Özgür and Nİhal Taş
Mathematical Sciences, 2017, Volume 11, Number 1, Page 7
[12]
Vahid PARVANEH, Nawab HUSSAIN, and Zoran KADELBURG
Acta Mathematica Scientia, 2016, Volume 36, Number 5, Page 1445
[13]
Wutiphol Sintunavarat
Journal of Fixed Point Theory and Applications, 2016, Volume 18, Number 2, Page 397
[14]
Oratai Yamaod, Wutiphol Sintunavarat, and Yeol Je Cho
Fixed Point Theory and Applications, 2015, Volume 2015, Number 1
[15]
Poom Kumam, Wutiphol Sintunavarat, Shaban Sedghi, and Nabi Shobkolaei
Journal of Function Spaces, 2015, Volume 2015, Page 1
[16]
Jamal R Roshan, Vahid Parvaneh, Stojan Radenović, and Miloje Rajović
Fixed Point Theory and Applications, 2015, Volume 2015, Number 1

Comments (0)

Please log in or register to comment.
Log in