Fixed Point Theorems for Generalized F-Contractions and Generalized F-Suzuki-Contractions in Complete Dislocated Sb-Metric Spaces

Mehravaran, Hamid; Khanehgir, Mahnaz; Allahyari, Reza

doi:10.28924/2291-8639-17-2019-734

Research Article

Fixed Point Theorems for Generalized F-Contractions and Generalized F-Suzuki-Contractions in Complete Dislocated Sb-Metric Spaces

Hamid Mehravaran¹
Mahnaz Khanehgir¹*
Reza Allahyari¹

Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

* Corresponding author

Abstract

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.

How to Cite

H. Mehravaran, M. Khanehgir, R. Allahyari, Fixed Point Theorems for Generalized F-Contractions and Generalized F-Suzuki-Contractions in Complete Dislocated Sb-Metric Spaces, Int. J. Anal. Appl. 17 (2019), 734–751. https://doi.org/10.28924/2291-8639-17-2019-734

BibTeX

@article{Mehravaran2019,
  author  = {Mehravaran, Hamid and Khanehgir, Mahnaz and Allahyari, Reza},
  title   = {Fixed Point Theorems for Generalized F-Contractions and Generalized F-Suzuki-Contractions in Complete Dislocated Sb-Metric Spaces},
  journal = {Int. J. Anal. Appl.},
  volume  = {17},
  year    = {2019},
  pages   = {734--751},
  doi     = {10.28924/2291-8639-17-2019-734}
}

References

[1] I. A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal. Unianowsk Gos. Ped. Inst. 30 (1989), 26-37.
[2] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostra. 1 (1993), 5-11.
[3] 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.
[4] 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.
[5] H. Piri and P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl. 2014 (2014), 210.
[6] 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 .
[7] N.Y. Ozgur and N. TaS ¸, Some fixed point theorems on S-metric spaces, Mat. Vesnik 69 (1) (2017), 39-52. ¨
[8] 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.
[9] 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.
[10] 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.
[11] Sh. Sedghi, N. Shobe and A. Aliouche, A generalization of fixed point theorem in S-metric spaces, Mat. Vesn. 64 (2012), 258-266.
[12] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012 (2012), 94.
[13] D. Wardowski and N.V. Dung, Fixed points of F-weak contractions on complete metric spaces, Demonstr. Math. 47 (1) (2014), 146-155.