Some common coupled fixed point theorems for generalized contraction in $b$-metric spaces

Volume 8, Issue 1, pp 8--16
• 995 Views

Authors

Nidhi Malhotra - Department of Mathematics, Hindu College, University of Delhi, Delhi, India. Bindu Bansal - Department of Mathematics, Hindu College, University of Delhi, Delhi, India.

Abstract

The aim of this paper is to prove the existence and uniqueness of a common coupled fixed point for a pair of mappings in a complete $b$-metric space in view of diverse contractive conditions. In addition, as a bi-product we obtain several new common coupled fixed point theorems.

Keywords

• Common fixed point
• coupled fixed point
• coupled coincidence point
• contractive mappings
• b-metric spaces.

•  47H10
•  54H25

References

• [1] M. Akkouchi, A common fixed point theorem for expansive mappings under strict implicit conditions on b-metric spaces, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math., 50 (2011), 5-15.

• [2] H. Aydi, M. F. Bota, E. Karapinar, S. Mitrović, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl., 2012 (2012), 8 pages.

• [3] I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, Functional Analysis, 30 (1989), 26-37.

• [4] M. Boriceanu, Fixed point theory for multivalued generalized contraction on a set with two b-metrics, Studia Univ. Babes-Bolyai Math., 3 (2009), 1-14.

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

• [6] T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis: TMA, 65 (2006), 1379-1393.

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

• [8] M. Jovanović, Z. Kadelburg, S. Radenović, Common fixed point results in metric-type spaces, Fixed Point Theory Appl., 2010 (2010), 15 pages.

• [9] M. Kir, H. Kiziltunc, On some well known fixed point theorems in b-metric spaces, Turkish J. Anal. Number Theory, 1 (2013), 13-16.

• [10] M. O. Olatinwo, C. O. Imoru, A generalization of some results on multi-valued weakly Picard mappings in b-metric space, Fasciculi Mathematici, 40 (2008), 45-56.

• [11] M. Păcurar , A fixed point result for $\phi$-contractions on b- metric spaces without the boundedness assumption , Fasc. Math., 43 (2010), 127-137.