Document Type : Research Paper


1 School of Mathematics, Thapar University, Patiala-147004, India.

2 School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, PR China.

3 Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, Serbia.


Compared with the previous work, the aim of  this paper is to introduce the more general concept of the generalized $F$-Suzuki type contraction mappings in $b$-metric spaces, and to establish some fixed point theorems in the setting of $b$-metric spaces. Our main results unify, complement and generalize the previous works in the existing literature.


Main Subjects

[1] M. Abbas, M. Berzig, T. Nazir, and E. Karapinar, Iterative approximation of fixed points for presic type $F$-contraction operators, Uni. Pol. Bucharest Sci. Bul. A-Appl. Math. Phy., 78 (2) (2016), pp. 147-160.
[2] H.H. Alsulami, E. Karapinar, and H. Piri, Fixed points of generalized F-Suzuki type contraction in complete $b$-metric spaces, Dis. Dyn. Nat. Soc., Volume 2015, Article ID 969726, 8 pages.
[3] H.H. Alsulami, E. Karapinar, and H. Piri, Fixed points of modified $F$-contractive mappings in complete metric-like spaces, J. Funct. Spaces, Volume 2015, Article ID 270971, 9 pages.
[4] I.A. Bakhtin, The contraction principle in quasimetric spaces, Funct. Anal., 30 (1989), pp. 26-37.
[5] L. Ciric, S. Chandok, and M. Abbas, Invariant approximation results of generalized nonlinear contractive mappings, Filomat, 30 (2016), pp. 3875-3883.
[6] S. Czerwik, Contraction mappings in $b$-metric spaces, Acta Math. Inform. Univ. Ostrav., 1 (1993), pp. 5-11.
[7] H. Ding, M. Imdad, S. Radenovic, and J. Vujakovic, On some fixed point results in $b$-metric, rectangular and $b$-rectangular metric spaces, Arab J. Math. Sci., 22 (2016), pp. 151-164.
[8] N.V. Dung, and V.L. Hang, A fixed point theorem for generalized $F$-contractions on complete metric spaces, Vietnam J. Math., 43 (2015), pp. 743-753.
[9] M. Jovanovic, Z. Kadelburg, and S. Radenovic, Common fixed point results in metric-type spaces, Fixed Point Theory Appl., Volume 2010, Article ID 978121, 15 pages.
[10] E. Karapinar, M.A. Kutbi, H. Piri, and D. ORegan, Fixed points of conditionally $F$-contractions in complete metric-like spaces, Fixed Point Theory Appl., 2015 (2015), Article ID 126, 14 pages.
[11] 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), Article ID 90, 13 pages.
[12] S. Shukla, S. Radenovic, and Z. Kadelburg, Some fixed point theorems for ordered $F$-generalized contractions in 0-$f$-orbitally complete partial metric spaces, Theory Appl. Math. Comput. Sci., 4 (2014), pp. 87-98.
[13] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), Article ID 94, 11 pages.
[14] D. Wardowski, and N.V. Dung, Fixed points of $F$-weak contractions on complete metric spaces, Demonstratio Math., 67 (2014), pp. 146-155.