New Fixed Point Results for Rational Type Contractions in Partially Ordered b-Metric Spaces
Main Article Content
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.
Article Details
References
- 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.
- 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.
- 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.
- 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.
- 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.
- V. Berinde, Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory, 1993, 3-9.
- TG. Bhaskar, V. Lakshmikantham, Fixed point theory in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379-1393.
- M. Boriceanu, M. Bota and A. Petrusel, Multivalued fractals in b-metric spaces, Cent. Eur. J. Math., 8 (2010), 367-377.
- 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.
- 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.
- S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), 263-276.
- S. Czerwik, Contraction mappings in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis, 1(1993), 5-11.
- B.K. Dass, S. Gupta, An extension of Banach contraction principle through rational expressions. Indian J. Pure Appl. Math., 6 (1975), 1455-1458.
- 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.
- D. S. Jaggi, Some unique fixed point theorems, Indian Journal of Pure and Applied Mathematics, 8 (1977), 223-230.
- 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.
- 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.