SOME FIXED POINT RESULTS ON EXTENDED
b-METRIC SPACES BY UTILIZING C-CLASS FUNCTIONS
Said Atallaoui1, Abdalla Tallafha1, Wasfi Shatanawi2,3
1 Department of Mathematics, School of Science
The University of Jordan, Amman 11942, JORDAN
2 Department of Mathematics and General Courses
Prince Sultan University
Riyadh 11586, SAUDI ARABIA
3 Department of Mathematics
Hashemite University, Zarqa, JORDAN

Abstract

In this paper, we employ the concept of C-class functions to prove some fixed point results in the setting of an extended b-metric space. Our result extend and generalize many existing results in the literature. Moreover, we introduce an example to show the validity of our results.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 33
Issue: 6
Year: 2020

DOI: 10.12732/ijam.v33i6.5

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References

  1. [1] A.H. Ansari, Note on ϕ-ψ-contractive type mappings and related fixed point, In: The 2nd Regional Conference on Mathematics and Applications, Payame Noor University, 2014 (2014), 377-380.
  2. [2] I.A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal., Gos. Ped. Inst., Unianowsk, 30 (1989), 26-37.
  3. [3] S. Banach, Sur les op´eration dans les ensembles abstraits et leur application aux ´equations int´egral, Fund. Math., 3 (1922), 133-181.
  4. [4] A. Bataihah, W. Shatanawi, A. Tallafha, Fixed point results with simulation functions, Nonlin. Funct. Anal. and Appl., 25, No 1 (2020), 13-23.
  5. [5] A. Bataihah, A. Tallafha, W. Shatanawi, Fixed point results with −distance by utilizing simulation functions, Italian J. of Pure and Appl. Math., 43 (2020), 185-196.
  6. [6] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav., 1 (1993), 5-11.
  7. [7] T. Kamran, M. Samreen, Q.U. Ain, A generalization of b-metric space and some fixed point theorems, Mathematics, 19, No 5 (2017), Art. 19.
  8. [8] M.S. Khan, M. Swaleh, S. Sessa, Fixed point theorems by altering distances between the points, Bull. of Austral. Math. Soc., 30 (1984), 1-9.
  9. [9] A. Mukheimer, N. Mlaiki, K. Abodayeh, W. Shatanawi, New theorems on extended b-metric spaces under new contractions. Nonlin. Anal.-Modeling and Control, 24, No 6 (2019), 870-883.
  10. [10] H. Qawaqneh, M.S.M. Noorani, W. Shatanawi, Fixed point theorems for (α, k, θ)-contractive multi-valued mapping in b-metric space and applications. Int. J. Math. Comput. Sci., 4 (2019), 263-283.
  11. [11] T. Qawasmeh, A. Tallafha, and W. Shatanawi, Fixed point theorems through modified ω−distance and application to nontrivial equations, Axioms , 8, No 2 (2019), Art. 57.
  12. [12] J.R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei, W. Shatanawi, Common fixed points of almost generalized (ψ,ϕ)s-contractive mappings in ordered b-metric spaces, Fixed Point Theory and Appl., 2013, No 1 (2013), Art. 159.
  13. [13] W. Shatanawi, M. Postolache, Common fixed point results for mappings under nonlinear contraction of cyclic form in ordered metric spaces, Fixed Point Theory Appl., 2013 (2013), Art. 60.
  14. [14] W. Shatanawi, Fixed and common fixed point for mapping satisfying some nonlinear contraction in b-metric spaces, J. Math. Anal., 7, No 4 (2016), 1-12.
  15. [15] W. Shatanawi, K. Abodayeh, A. Mukheimer, Some fixed point theorems in extended b-metric spaces, Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar., 80, No 4 (2018), 71-78.
  16. [16] W. Shatanawi, A. Pitea, R. Lazovi´c, Contraction conditions using comparison functions on b-metric spaces, Fixed Point Theory Appl., 2014 (2014), Art. 135.
  17. [17] W. Shatanawi, M. Postolache, Coincidence and fixed point results for generalized weak contractions in the sense of Berinde on partial metric spaces, Fixed Point Theory Appl., 2013 (2013), Art. 54.
  18. [18] A.H. Ansari, W. Shatanawi, C-class functions on fixed and common fixed point results for cyclic mappings of Omega-distance. Nonlin. Anal.Modeling and Control, 22, No 6 (2017), 739-752.