Main Article Content
In this paper, first we describe the notion of dislocated Sb-metric space and then we introduce the new notions of generalized F-contraction and generalized F-Suzuki-contraction in the setup of dislocated Sb-metric spaces. We establish some fixed point theorems involving these contractions in complete dislocated Sb-metric spaces. We also furnish some examples to verify the effectiveness and applicability of our results.
- I. A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal. Unianowsk Gos. Ped. Inst. 30 (1989), 26-37.
- S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostra. 1 (1993), 5-11.
- N.V. Dung and V.L. Hang, A fixed point theorem for generalized F-contractions on complete metric spaces, Vietnam J. Math. 43 (2015), 743-753.
- G.N.V. Kishore, K.P.R. Rao, D. Panthi, B. Srinuvasa Rao and S. Satyanaraya, Some applications via fixed point results in partially ordered Sb-metric spaces, Fixed Point Theory Appl. 2017 (2017), 10.
- H. Piri and P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl. 2014 (2014), 210.
- H. Piri and P. Kumam, Fixed point theorems for generalized F-Suzuki-contraction mappings in complete b-metric spaces, Fixed Point Theory Appl. 2016 (2016), 90 .
- N.Y. Ozgur and N. TaS ¸, Some fixed point theorems on S-metric spaces, Mat. Vesnik 69 (1) (2017), 39-52. ¨
- N.Y. Ozgur, N. TaS ¸ and U. Celik, New fixed point-circle results on ¨ S-metric spaces, Bull. Math. Anal. Appl. 9 (2) (2017), 10-23.
- Y. Rohena, T. Dosenovic and S. Radenovic, A note on the paper ”A Fixed point Theorems in Sb-Metric Spaces”, Filomal 31 (11) (2017), 3335-3346.
- Sh. Sedghi, A. Gholidahne, T. Dosenovic, J. Esfahani and S. Radenovic, Common fixed point of four maps in Sb-metric spaces, J. Linear Topol. Alg. 5 (2) (2016), 93-104.
- Sh. Sedghi, N. Shobe and A. Aliouche, A generalization of fixed point theorem in S-metric spaces, Mat. Vesn. 64 (2012), 258-266.
- D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012 (2012), 94.
- D. Wardowski and N.V. Dung, Fixed points of F-weak contractions on complete metric spaces, Demonstr. Math. 47 (1) (2014), 146-155.