Various Suzuki type theorems in \(b\)-metric spaces

Volume 8, Issue 4, pp 363--377 http://dx.doi.org/10.22436/jnsa.008.04.09

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Authors

A. Latif - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia. V. Parvaneh - Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran. P. Salimi - Young Researchers and Elite Club, Rasht Branch, Islamic Azad University, Rasht, Iran. A. E. Al-Mazrooei - Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.

Abstract

In this paper, we prove some fixed point results for \(\alpha\)-admissible mappings which satisfy Suzuki type contractive condition in the setup of b-metric spaces. Finally, examples are presented to verify the effectiveness and applicability of our main results.

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Keywords

• Ordered metric space
• b-metric space
• fixed point.

MSC

•  47H10
•  54H25

References

• [1] A. Aghajani, M. Abbas, J. R. Roshan , Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 64 (2014), 941-960.


• [2] V. Berinde, Generalized contractions in quasi-metric spaces, Seminar on Fixed Point Theory, Preprint, 3 (1993), 3-9.


• [3] V. Berinde, Sequences of operators and fixed points in quasi-metric spaces, Studia Universitatis Babes-Bolyai, Mathematica, 16 (1996), 23-27.


• [4] V. Berinde, Contracţii generalizate şi aplicaţii , Editura Club Press, Baia Mare (1997)


• [5] F. Bojor, Fixed point theorems for Reich type contraction on metric spaces with a graph, Nonlinear Anal., 75 (2012), 3895-3901.


• [6] M. Boriceanu , Fixed point theory for multivalued generalized contractions on a set with two b-metrics, Studia Univ. ''Babes-Bolyai'', Mathematica, Vol. LIV, No. 3 (2009)


• [7] M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, Int. J. Modern Math., 4 (2009), 285-301.


• [8] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inf. Univ. Ostrav., 1 (1993), 5-11.


• [9] S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), 263-276.


• [10] D. Dukić, Z. Kadelburg, S. Radenović, Fixed points of Geraghty-type mappings in various generalized metric spaces, Abstr. Appl. Anal., 2011 (2011), 13 pages.


• [11] M. Edelstein, On fixed and periodic points under contractive mappings , J. London Math. Soc., 37 (1962), 74-79.


• [12] M. Geraghty, On contractive mappings , Proc. Amer. Math. Soc., 40 (1973), 604-608.


• [13] N. Hussain, D. Đorić, Z. Kadelburg, S. Radenović, Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl., 2012 (2012), 12 pages.


• [14] D. S. Jaggi , Some unique fixed point theorems , Indian J. Pure Appl. Math., 8 (1977), 223-230.


• [15] J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136 (2008), 1359-1373.


• [16] M. A. Khamsi, N. Hussain, KKM mappings in metric type spaces, Nonlinear Anal., 73 (2010), 3123-3129.


• [17] E. Karapınar, P. Kumam, P. Salimi, On \(\alpha-\psi\)-Meir-Keeler contractive mappings, Fixed Point Theory Appl., 2013 (2013), 12 pages.


• [18] H. K. Nashine, M. Imdad, M. Hasanc, Common fixed point theorems under rational contractions in complex valued metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 42-50.


• [19] J. J. Nieto, R. R. Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223-239.


• [20] M. Ozturk, M. Basarir, On some common fixed point theorems with rational expressions on cone metric spaces over a Banach algebra, Hacet. J. Math. Stat., 41 (2012), 211-222.


• [21] A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435-1443.


• [22] J. R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei, W. Shatanawi, Common fixed points of almost generalized \((\psi,\varphi )_s\)-contractive mappings in ordered b-metric spaces , Fixed Point Theory Appl., 2013 (2013), 23 pages.


• [23] B. Samet, C. Vetro, P. Vetro, Fixed point theorem for \(\alpha-\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165.


• [24] P. Salimi, E. Karapınar, Suzuki-Edelstein type contractions via auxiliary functions , Math. Probl. Eng., 2013 (2013), 8 pages.


• [25] R. J. Shahkoohi, A. Razani , Some fixed point theorems for rational Geraghty contractive mappings in ordered b-metric spaces, J. Inequal. Appl., 2014 (2014), 23 pages.


• [26] T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 136 (2008), 1861-1869.


• [27] T. Suzuki , A new type of fixed point theorem in metric spaces, Nonlinear Anal.-TMA, 71 (2009), 5313-5317.


• [28] F. Zabihi, A. Razani , Fixed point theorems for Hybrid rational Geraghty contractive mappings in ordered b-metric spaces, J. Appl. Math., 2014 (2014), 9 pages.