GREGUS TYPE COMMON FIXED POINT THEOREMS in b-METRIC SPACE with APPLICATION

Rakesh Tiwari; Sudhir Kumar Srivastava; Savita Gupta; Shobha Rani

doi:https://doi.org/10.14445/22315373/IJMTT-V66I7P515

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 7 | Year 2020 | Article Id. IJMTT-V66I7P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I7P515

GREGUS TYPE COMMON FIXED POINT THEOREMS in b-METRIC SPACE with APPLICATION

Rakesh Tiwari, Sudhir Kumar Srivastava, Savita Gupta, Shobha Rani

Citation :

Rakesh Tiwari, Sudhir Kumar Srivastava, Savita Gupta, Shobha Rani, "GREGUS TYPE COMMON FIXED POINT THEOREMS in b-METRIC SPACE with APPLICATION," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 7, pp. 112-120, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I7P515

Abstract

The aim of this paper is to establish Gregus Type common fixed point theorems in b-metric spaces. Our results improve and extend some known results. An example is given to show that our results are proper generalizations of the existing ones and we also provide an application.

Keywords

Fixed point, Common fixed point, b-metric space, b-compatible.

References

[1] A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal., Ulianowsk Gos. Ped. Inst.,30(1989), 26-37.
[2] Banach, S. Surles operations dens les ensembles abstract et leur application aux equation integrals, Fund. Math. 3(1922), 133-181.
[3] S. Czerwik, Contraction mapping in b-metric space, Acta Math. Inform. Univ. Ostrav., 1 (1993), 5-11.
[4] N. V. Dung, V. T. L. Hang, On relaxation of contraction constsnts and Caristis theorem in b-metric spaces, J. Fixed Point TheoryAppl. 18(2016), 267-284.
[5] B. Fisher, Four mappings with a common fixed point, The Journal of the University of Kuwait. Science, 8, (1981), 131-139.
[6] N. Hussain, D. Djoric, Z. Kadelburg and S. Radenovic, Suzuki-type fixed point result in metric spaces, Fixed Point Theory Appl., (2012):126.
[7] N. Hussain, Z. D. Mitrovic, On multi-valued weak quasi-contruction in b-metric spaces, J. Nonlinear Sci. Appl. , (2017), 3815-3823.
[8] N. Hussain, Z. D. Djoric, and S. Radenovic, A common fixed point theorem of Fisher in b-metric spaces, Springer Link Volume 113, Issue 2, pp (2018) 949956.
[9] M. H. Shah and N. Hussain, KKM mapping in cone b-metric spaces, Comput. math. Appl., 62 (2011) 1677- 1684.
[10] M. Jovanovic, Z. Kadelburg, S. Radenovic, Common fixed point result in Metric type spaces, Fixed Point Theory Appl. (2010), Article ID 978121, 15P.3.
[11] G. Jungck, Commuting mappings and fixed points, Am. Math. Mon. 83, (1976), 261-263.
[12] G. Jungck, Compatible mappings and Common fixed points, Internet J. Math. Sci. 9 (1986), 771-779.
[13] M. A. Khamsi, N. Hussain, KKM mappings in metric type spaces, Nonlinear Anal., 73 (2010), 3123-3129.
[14] R. Miculescu, A. Mihail, New fixed point theorem for set-valued contractions in b-metric spaces, J. Fixed Point Theory Appl. DOI 10. 1007/s11784-016-0400-2, 2017.
[15] Z. D. Mitrovic, S. Radenovic, A common fixed point theorem of Jungck in rectengular b-metric spaces, Acta Math.Hunger. (2017). doi.org/10.1007/s10474-017-0750-2.
[16] J. R. Roshan, N. Shobkolaei, S. Sedhgi, M. Abbas, Common fixed point of four maps in b-metric spaces Hacet. J. Math.Stat. 43. No. 4, (2014), 613-624.