Title: New Fixed Point Results for Rational Type Contractions in Partially Ordered b-Metric Spaces
Author(s): Reza Arab, Kolsoum Zare
Pages: 64-70
Cite as:
Reza Arab, Kolsoum Zare, New Fixed Point Results for Rational Type Contractions in Partially Ordered b-Metric Spaces, Int. J. Anal. Appl., 10 (2) (2016), 64-70.

Abstract


The purpose of this paper is to establish some fixed point theorems for a mapping having a monotone property satisfying a contractive condition of rational type in the partially ordered b-metric spaces. The results presented in the paper generalize and extend several well-known results in the literature. An example is given to support the usability of our results.

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References


  1. A. Aghajani, M. Abbas and J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b−metric spaces, Mathematica Slovaca, 64 (2014), 941-960. Google Scholar

  2. A. Aghajani, R. Arab, Fixed points of (ψ,ϕ,θ)-contractive mappings in partially ordered b−metric spaces and application to quadratic integral equations, Fixed Point Theory and Applications, 2013 (2013), Article ID 245. Google Scholar

  3. R. Allahyari, R. Arab, A. Shole Haghighi, A generalization on weak contractions in partially ordered b−metric spaces and its application to quadratic integral equations, Journal of Inequalities and Applications, 2014 (2014), Article ID 355. Google Scholar

  4. R. Allahyari, R. Arab, A. Shole Haghighi, Fixed points of admissible almost contractive type mappings on b− metric spaces with an application to quadratic integral equations, Journal of Inequalities and Applications, 2015 (2015), Article ID 32. Google Scholar

  5. H. Aydi, M. F. Bota, E. Karapinar and S. Moradi, A common fixed point for weak ϕ−contractions on b−metric spaces, Fixed Point Theory, 13 (2012), 337-346. Google Scholar

  6. V. Berinde, Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory, 1993, 3-9. Google Scholar

  7. TG. Bhaskar, V. Lakshmikantham, Fixed point theory in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379-1393. Google Scholar

  8. M. Boriceanu, M. Bota and A. Petrusel, Multivalued fractals in b−metric spaces, Cent. Eur. J. Math., 8 (2010), 367-377. Google Scholar

  9. I. Cabrera, J. Harjani, K. Sadarangani, A fixed point theorem for contractions of rational type in partially ordered metric spaces. Ann. Univ. Ferrara, 59 (2013), 251-258. Google Scholar

  10. S. Chandok, T. D. Narang, M. Taoudi,Fixed point theorem for generalized contractions satisfying rational type expressions in partially ordered metric spaces, Gulf Journal of Mathematics, 2 (2014), 87-93. Google Scholar

  11. S. Czerwik, Nonlinear set-valued contraction mappings in b−metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), 263-276. Google Scholar

  12. S. Czerwik, Contraction mappings in b−metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis, 1(1993), 5-11. Google Scholar

  13. B.K. Dass, S. Gupta, An extension of Banach contraction principle through rational expressions. Indian J. Pure Appl. Math., 6 (1975), 1455-1458. Google Scholar

  14. J.Harjani, B. Lopez, and K. Sadarangani, A fixed point theorem for mappings satisfying a contractive condition of rational type on a partially orderedmetric space, Abstract and Applied Analysis, 2010 (2010), Article ID 190701. Google Scholar

  15. D. S. Jaggi, Some unique fixed point theorems, Indian Journal of Pure and Applied Mathematics, 8 (1977), 223-230. Google Scholar

  16. M. Pacurar, Sequences of almost contractions and fixed points in b−metric spaces, Anal. Univ. de Vest, Timisoara Seria Matematica Informatica, 48 (2010), 125-137. Google Scholar

  17. M-A. Kutbi, E. Karapnar, J. Ahmad, A. Azam, Some fixed point results for multi-valued mappings in b−metric spaces. J. Inequal. Appl. 2014 (2014), Article ID 126. Google Scholar


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