FIXED POINT RESULTS FOR MAPPINGS
SATISFYING CONTRACTIVE CONDITIONS
BUILD ON COUPLED-$\alpha$-ADMISSIBILITY
Wasfi Shatanawi1,2, Kamaleldin Abodyeh1
1Department of Mathematics
Prince Sultan University
Riyadh, SAUDI ARABIA
2Department of Medical Research
China Medical University Hospital
China Medical University, Taichung, TAIWAN

Abstract

We consider in this article the notions of coupled$-\alpha-$contraction of types (I) and (II) for a mapping $F$ defined on a set $\Psi\times\Psi$. Many fixed point (FP) results in the domain of metric space are obtained using our new notions. The obtained results are used to modify some known FP theorems. Some example are given to show the authenticity of our new definitions.

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: 2
Year: 2020

DOI: 10.12732/ijam.v33i2.2

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References

  1. [1] T. Abdeljawad, Meir-Keeler -contractive fixed and common fixed point theorems. Fixed Point Theory Appl., 2013 (2013), 10 pages.
  2. [2] T. Abdeljawad, J. Alzabut, A. Mukheimer, Y. Zaidan, Best proximity points for cyclical contraction mappings with 0-boundedly compact decompositions, J. of Computational Analysis and Applications, 15, No 4 (2013), 678–685.
  3. [3] T. Abdeljawad, J. Alzabut, A. Mukheimer, Y. Zaidan, Banach contraction principle for cyclical mappings on partial metric spaces, Fixed Point Theory and Applications, 2012 (2012), Art. ID 154.
  4. [4] K. Abodayeh, W Shatanawi, A Bataihah, AH Ansari, Some fixed point and common fixed point results through -distance under nonlinear contractions, Gazi University J. of Science, 30, No 1 (2017), 293–302.
  5. [5] A. Al-Rawashdeha, H. Aydi, F. Abdelbasset, S. Sahmim, W. Shatanawi, On common fixed points for −F−contractions and applications, J. Nonlinear Sci. Appl., 9 (2016), 3445–3458.
  6. [6] A.H. Ansari, J. Kaewcharoen, C-class functions and fixed point theorems for generalized −− −'−F-contraction type mapping in −-complete metric space, Nonlinear Sci. Appl., 9 (2016), 4177–4190.
  7. [7] H. Aydi, E. Karapinar, and W. Shatanawi, Tripled common fixed point results for generalized contractions in ordered generalized metric spaces, Fixed Point Theory and Applications, 2012, No 1 (2012), Art. ID 101.
  8. [8] H. Aydi, W. Shatanawi, M. Postolache, Z. Mustafa, and N. Tahat, Theorems for Boyd-Wong type contractions in ordered metric spaces, Abstract and Applied Analysis 2012 (2012), Art. ID 359054, 14 pages.
  9. [9] S. Banach, Sur les op´erations dans les ensembles et leur application aux equations itegrales, Fundam. Math. 3 (1922), 133–181.
  10. [10] Y.J. Cho, Z. Kadelburg, R. Saadati, and W. Shatanawi, Coupled fixed point theorems under weak contractions, Discrete Dynamics in Nature and Society, 2012 (2012), Art. ID 184534, 9 pages; doi:10.1155/2012/184534.
  11. [11] N. Hussain, M. Arshad, A. Shoaib, Fahimuddin, Common fixed point results for - -contractions on a metric space endowed with graph, J. of Inequalities Appl., 2014 (2014), Art. ID 136.
  12. [12] N. Hussain, M.A. Kutbi, P. Salimi, Fixed point theory in −complete metric spaces with applications, Abstr. Appl. Anal., 2014 (2014), 11 pages, 1, 1.16, 1.18.
  13. [13] N. Hussain, P. Salimi and A. Latif, Fixed point results for single and setvalued a −− − contractive mappings, Fixed Point Theory Appl., 2013 (2013), Art. ID 212.
  14. [14] E. Karapinar, P. Kumam and P. Salimi, On − −Meir-Keeler contractive mappings, Fixed Point Theory Appl., 2013 (2013), Art. ID 94.
  15. [15] H. Qawagneh, M.S. Noorani, W. Shatanawi, K. Abodayeh and H. Alsamir, Fixed point for mappings under contractive condition based on simulation functions and cyclic ( − )-admissibility, J. of Mathematical Analysis, 9, No 1 (2018), 38–51.
  16. [16] T. Qawasmeh, W. Shatanawi, A. Bataihah and A. Tallafha, Common fixed point results for rational ( , )'−contractions in complete quasi metric spaces, Mathematics, 7, No 5 (2019), Art. ID 392; doi:10.3390/math7050392.
  17. [17] P. Salimi, A. Latif and N. Hussain, Modified − −Contractive mappings with applications, Fixed Point Theory Appl., 2013 (2013), Art. ID 151.
  18. [18] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for an − -contractive type mappings, Nonlinear Anal., 75 (2012), 2154–2165.
  19. [19] W. Shatanawi, Fixed and common fixed point theorems in frame of quasi metric spaces under contraction condition based on ultra distance functions, Nonlinear Analysis: Modelling and Control, 23, No 5 (2018), page 724.
  20. [20] W. Shatanawi, K. Abodayeh, Common fixed point for mappings under contractive condition based on almost perfect functions and -admissibility, Nonlinear Functional Analysis and Applications, 23 (2018), 247–257.
  21. [21] W. Shatanawi, and K. Abodayeh, Fixed point results for mapping of nonlinear contractive conditions of −admissibility form, IEEE Access, 7 (2019) 50280–50286; doi:10.1109/ACCESS.2019.2910794.
  22. [22] W. Shatanawi, and K. Abodayeh, Common fixed point under nonlinear contractions on quasi metric spaces, Mathematics, 2019, No 7 (2019), Art. ID 453.
  23. [23] W. Shatanawi, and K. Abodayeh, Some fixed and common fixed point results in g-metric spaces which cannot be obtained from metric spaces, Boletim da Sociedade Paranaense de Matematica, 38, No 6 (2020), 4–51.
  24. [24] W. Shatanawi, K. Abodayeh, and A. Bataihah, Fixed point theorem through −distance of Suzuki type contraction condition, Gazi University J. of Science, 29, No 1 (2016), 129–133.
  25. [25] W. Shatanawi, K. Abodayeh, A. Mukheimer, Some fixed point theorems in extended b-metric spaces, U.P.B. Sci. Bull., Series A, 80, No 4 (2018).
  26. [26] W. Shatanawi, A. Al-Rawashdeh, Common fixed points of almost generalized ( , )−contractive mappings in ordered metric spaces, Fixed Point Theory and Applications, 2012, No 1 (2012), Art. ID 80.
  27. [27] W. Shatanawi, Z Mustafa, N Tahat, Some coincidence point theorems for nonlinear contraction in ordered metric spaces, Fixed point Theory and applications, 2011, No 1 (2011), Art. ID 68.
  28. [28] W. Shatanawi, Z.D. Mitrovic, N. Hussain and S. Radenovic, On generalized hardy rogers type −admissible mappings in cone b-metric spaces over Banach algebras, Symmetry, 2020, No 12 (2020), Art. ID 81; doi:10.3390/sym12010081.
  29. [29] W. Shatanawi, M.S. MD Noorani, H. Alsamir, A. Bataihah, Fixed and common fixed point theorems in partially ordered quasimetric spaces, J. Math. Computer Sci., 16 (2016), 516–528.
  30. [30] 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 and Applications 2013 (2013), Art. ID 54.
  31. [31] W. Shatanawi, M. Postolache, Some fixed-point results for a-weak contraction in-metric spaces, Abstract and Applied Analysis, 2012 (2012), Art. ID 815870, 19 pages.