Common Fixed Points for (𝝍,𝓕,𝜶,𝜷)-Weakly Contractive Mappings in Generalized Metric Spaces via New Functions

Year 2015, Volume: 28 Issue: 4, 703 - 708, 16.12.2015

Huseyin Isık , Arslan H. Ansari , Sumit Chandok Duran Turkoglu

https://izlik.org/JA83PF94HC

Abstract

In this article, we establish some common fixed point theorems for some new contractive mappings involving new function classes in generalized metric spaces. We provide an example in order to support the useability of our results. These results generalize some well-known results in the literature.

Keywords

Fixed point , C-class functions , generalized metric , weakly contractive

References

• A. Branciari, A fixed point theorem of Banach- Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen. 57 (2000) 31-37.
• H. Isik, D. Turkoglu, Common fixed points for ( , , )-weakly generalized metric spaces, Fixed Point Theory and Applications 2013, 2013:131. mappings in
• P. Das, A fixed point theorem in a generalized metric space, Soochow J. Math. 33 (1) (2007) 33- 39.
• P. Das, B.K. Lahiri, Fixed point of a Ljubomir Ćirić's quasi-contraction mapping in a generalized metric space, Publ. Math. Debrecen. 61 (2002) 589-594.
• P. Das, B.K. Lahiri, Fixed point of contractive mappings in generalized metric spaces, Math. Slovaca 59 (4) (2009) 499-504.
• A. Fora, A. Bellour, A. Al-Bsoul, Some results in fixed point theory concerning generalized metric spaces, Mat. Vesnik 61 (3) (2009) 203-208.
• D. Mihet, On Kannan fixed point principle in generalized metric spaces, J. Nonlinear Sci. Appl. 2 (2) (2009) 92-96.
• B. Samet, A fixed point theorem in a generalized metric space for mappings satisfying a contractive condition of integral type, Int. J. Math. Anal. 3 (26) (2009) 1265-1271.
• B. Samet, Discussion on: a fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces by A. Branciari, Publ. Math. Debrecen. 76 (4) (2010) 493-494.
• I.R. Sarma, J.M. Rao, S.S. Rao, Contractions over generalized metric spaces, J. Nonlinear Sci. Appl. 2 (3) (2009) 180-182.
• H. Lakzian, B. Samet, Fixed point for ( , )- weakly contractive mappings in generalized metric spaces, Appl. Math. Lett. 25 (5) (2012) 902-906.
• C. Di Bari, P. Vetro, Common fixed points in generalized metric spaces, Appl. Math. Comp., 218 (13) (2012) 7322-7325.
• B. S. Choudhury, A. Kundu, ( , , )-weak contractions in partially ordered metric spaces, Appl. Math. Lett. 25 (1), (2012) 6-10.
• G. Jungck, B.E. Rhoades, Fixed point for set valued functions without continuity, Indian J. Pure Appl. Math. 29 (3) (1998) 227-238.
• Z. Kadelburg, S. Radenović, Fixed point results in generalized metric spaces without Hausdorff property, Math. Sci. (2014) 8:125.
• A.H. Ansari, Note on " - -contractive type mappings and related fixed point", The 2nd Regional Conference on Mathematics and Appl., 2014 (2014), 377-380.
• Z.M. Fadail, A.G.B. Ahmad, A.H. Ansari, S. Radenovic, M. Rajovic, Some common fixed point results of mappings in 0-complete metric-like spaces via new function, Applied Mathematical Sciences, 9 (2015), 4109-4127.
• A. Latif, H. Isik, A.H. Ansari, Fixed points and functional equation problems via cyclic admissible generalized Nonlinear Sci. Appl. (in press). type mappings, J.