Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SOME FIXED POINT RESULTS FOR TAC-SUZUKI CONTRACTIVE MAPPINGS

  • Mebawondu, Akindele A. (School of Mathematics, Statistics and Computer Science University of KwaZulu-Natal) ;
  • Mewomo, Oluwatosin T. (School of Mathematics, Statistics and Computer Science University of KwaZulu-Natal)
  • Received : 2018.10.11
  • Accepted : 2019.02.27
  • Published : 2019.10.31
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Abstract

In this paper, we introduce the notion of modified TAC-Suzuki-Berinde type F-contraction and modified TAC-(${\psi}$, ${\phi}$)-Suzuki type rational mappings in the frame work of complete metric spaces, we also establish some fixed point results regarding this class of mappings and we present some examples to support our main results. The results obtained in this work extend and generalize the results of Dutta et al. [9], Rhoades [18], Doric, [8], Khan et al. [13], Wardowski [25], Piri et al. [17], Sing et al. [23] and many more results in this direction.

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References

  1. C. T. Aage and J. N. Salunke, Fixed points for weak contractions in G-metric spaces, Appl. Math. E-Notes 12 (2012), 23-28.
  2. S. Banach, Sur les oprations dans les ensembles abstraits et leur application aux quations intgrales, Fundamenta Mathematicae 3 (1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181
  3. G. V. R. Babu and P. D. Sailaja, A fixed point theorem of generalized weakly contractive maps in orbitally complete metric spaces, Thai J. Math. 9 (2011), no. 1, 1-10.
  4. V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum 9 (2004), no. 1, 43-53.
  5. V. Berinde, General constructive xed point theorems for Ciric-type almost contractions in metric spaces, Carpathian J. Math. 24 (2008), no. 2, 10-19.
  6. S. Chandok, K. Tas, and A. H. Ansari, Some xed point results for TAC-type contractive mappings, J. Funct. Spaces 2016 (2016), Art. ID 1907676, 6 pp. https://doi.org/10.1155/2016/1907676
  7. B. S. Choudhury and C. Bandyopadhyay, Suzuki type common fixed point theorem in complete metric space and partial metric space, Filomat 29 (2015), no. 6, 1377-1387. https://doi.org/10.2298/FIL1506377C
  8. D. Doric, Common fixed point for generalized ($\psi$, $\phi$)-weak contractions, Appl. Math. Lett. 22 (2009), no. 12, 1896-1900. https://doi.org/10.1016/j.aml.2009.08.001
  9. P. N. Dutta and B. S. Choudhury, A generalisation of contraction principle in metric spaces, Fixed Point Theory Appl. 2008 (2008), Art. ID 406368, 8 pp. https://doi.org/10.1155/2008/406368
  10. X. Fan and Z. Wang, Some fixed point theorems in generalized quasi-partial metric spaces, J. Nonlinear Sci. Appl. 9 (2016), no. 4, 1658-1674. https://doi.org/10.22436/jnsa.009.04.22
  11. M. A. Geraghty, On contractive mappings, Proc. Amer. Math. Soc. 40 (1973), 604-608. https://doi.org/10.2307/2039421
  12. D. S. Jaggi, Some unique xed point theorems, Indian J. Pure Appl. Math. 8 (1977), no. 2, 223-230.
  13. M. S. Khan, M. Swaleh, and S. Sessa, Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc. 30 (1984), no. 1, 1-9. https://doi.org/10.1017/S0004972700001659
  14. J. Morales and E. Rojas, Some results on T-Zamrescu operators, Revista Notas de Matematics 5 (2009), no. 1, 64-71.
  15. J. Morales and E. Rojas, Some generalizations of Jungck's fixed point theorem, Int. J. Math. Math. Sci. 2012 (2012), Art. ID 213876, 19 pp. https://doi.org/10.1155/2012/213876
  16. P. P. Murthy, L. N. Mishra, and U. D. Patel, n-tupled fixed point theorems for weak-contraction in partially ordered complete G-metric spaces, New Trends Math. Sci. 3 (2015), no. 4, 50-75.
  17. H. Piri and P. Kumam, Some xed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl. 2014 (2014), 210, 11 pp. https://doi.org/10.1186/1687-1812-2014-210
  18. B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal. 47 (2001), no. 4, 2683-2693. https://doi.org/10.1016/S0362-546X(01)00388-1
  19. P. Salimi and P. Vetro, A result of Suzuki type in partial G-metric spaces, Acta Math. Sci. Ser. B (Engl. Ed.) 34 (2014), no. 2, 274-284. https://doi.org/10.1016/S0252-9602(14)60004-7
  20. B. Samet, C. Vetro, and P. Vetro, Fixed point theorems for ${\alpha}$-$\psi$-contractive type mappings, Nonlinear Anal. 75 (2012), no. 4, 2154-2165. https://doi.org/10.1016/j.na.2011.10.014
  21. N.-A. Secelean, Iterated function systems consisting of F-contractions, Fixed Point Theory Appl. 2013 (2013), 277, 13 pp. https://doi.org/10.1186/1687-1812-2013-277
  22. W. Shatanawi and M. Postolache, Some fixed-point results for a G-weak contraction in G-metric spaces, Abstr. Appl. Anal. 2012 (2012), Art. ID 815870, 19 pp.
  23. S. L. Singh, R. Kamal, M. De la Sen M, and R. Chugh, A fixed point theorem for generalized weak contractions, Filomat 29 (2015), no. 7, 1481-1490. https://doi.org/10.2298/FIL1507481S
  24. T. Suzuki, Fixed point theorems and convergence theorems for some generalized non-expansive mappings, J. Math. Anal. Appl. 340 (2008), no. 2, 1088-1095. https://doi.org/10.1016/j.jmaa.2007.09.023
  25. D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012 (2012), 94, 6 pp. https://doi.org/10.1186/1687-1812-2012-94
  26. F. Yan, Y. Su, and Q. Feng, A new contraction mapping principle in partially ordered metric spaces and applications to ordinary differential equations, Fixed Point Theory Appl. 2012 (2012), 152, 13 pp. https://doi.org/10.1186/1687-1812-2012-152