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FIXED POINT THEOREMS INVOLVING C-CLASS FUNCTIONS IN Gb-METRIC SPACES

  • HAMAIZIA, TAIEB (System Dynamics and Control Laboratory, Department of Mathematics and Informatics, Oum El Bouaghi University)
  • Received : 2020.09.01
  • Accepted : 2020.12.31
  • Published : 2021.05.30

Abstract

The purpose of this paper is to prove some fixed point theorems using (𝜓, 𝜑)-contractions via the concept of C-class functions in Gb-metric spaces. Moreover, an example is presented to illustrate the validity of our results.

Keywords

References

  1. M. Abbas, I.Z. Chema, A. Razani, Existence of common fixed point for b-metric rational type contraction, Filomat 30 (2016), 1413-1429. https://doi.org/10.2298/FIL1606413A
  2. M. Abbas, A.R. Khan and T. Nazir, Coupled common fixed point results in two generalized metric spaces, Appl. Math. Comput. 217 (2011), 6328-6336. https://doi.org/10.1016/j.amc.2011.01.006
  3. A. Aghajani, M. Abbas, J.R. Roshan, Common fixed point of generallized weak contractive mappings inpartially ordered Gb-metric spaces, Filomat 28 (2014), 1087-1101. https://doi.org/10.2298/FIL1406087A
  4. A.H. Ansari, Note on φ-ψ-contractive type mappings and related fixed point, The 2nd regional conference on mathematics and applications, Payame Noor University, 2014.
  5. A.H. Ansari, H. Aydi, P.S. Kumari and I. Yildirim, New Fixed Point Results via C-class Functions in b-Rectangular Metric Spaces, Commun. Math. Appl. 9 (2018), 109-126.
  6. A.H. Ansari, J. Kaewcharoen, C-class functions and fixed point theorems for generalized α-η-ψ-φ-F-contraction type mappings in α-η-complete metric spaces, J. Nonlinear Sci. Appl. 9 (2016), 4177-4190. https://doi.org/10.22436/jnsa.009.06.60
  7. A.H. Ansari, M.A. Barakat and H. Aydi, New Approach for Common Fixed Point Theorems via C-Class Functions in GP -Metric Spaces, J. Funct. Spaces 2017 (2017), 1-9.
  8. A.H. Ansari, H. Isik, S. Radenovic, Coupled Fixed Point Theorems for Contractive Mappings Involving New Function Classes and Applications, Filomat 34 (2017), 1893-1907.
  9. A.H. Ansari and A. Razani, Some fixed point theorems for C-class functions in b-metric spaces, Sahand Communications in Mathematical Analysis 10 (2018), 85-96.
  10. H. Aydi, D. Rakic, A. Aghajani, T. Dosenovic, M.S.M. Noorani and H. Qawaqneh, On Fixed Point Results in Gb-Metric Spaces, Mathematics 7 (2019), 1-19. https://doi.org/10.3390/math7010001
  11. I.A. Bakhtin, The contraction mapping principle in almost metric space. Funct. Anal. 30 (1989), 26-37.
  12. S. Chandok, V. Ozturk and S. Radenovic, On fixed points in the context of b-metric spaces, Mat. Vesnik 71 (2019), 23-30.
  13. V.S. Chary, G.S.M. Reddy, H. Isik, H. Aydi, D.S. Chary, S. Radenovic, Some fixed point theorems for modified JS-G-contractions and an application to integral equations, J. Appl. Math. & Informatics 38 (2020), 507-518. https://doi.org/10.14317/JAMI.2020.507
  14. S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform., Univ. Ostrav 1 (1993), 5-11.
  15. H. Isik, A.H. Ansari , D. Turkoglu, S. Chandok, Common Fixed Points for (ψ, $\mathbf{F}$, α, β)-Weakly Contractive Mappings in Generalized Metric Spaces via New Functions, GU J. Sci. 28 (2014), 703-708.
  16. Z. Kadelburg, L. Paunovic, S. Radenovic, A note on fixed point theorems for weakly T-Kannan and weakly T-Chatterjea contractions in b-metric spaces, Gulf J. Math. 3 (2015), 57-67.
  17. M.S. Khan, M. Swaleh and S. Sessa, Fixed point theorems by altering distances between the points, Bulletin of the Australian Mathematical Society 30 (1984), 1-9. https://doi.org/10.1017/S0004972700001659
  18. B. Khomdram, Y. Rohen, T.C. Singh, Couplede fixed point theorems in Gb-metric space satisfying some rational contractive conditions, SpringerPlus, 2016.
  19. P. Kumam, W. Sintunavarat, The existence of fixed point theorems for partial q-set-valued quasi-contractions in b-metric spaces and related results, Fixed Point Theory Appl. 2014 (2014), 1-20. https://doi.org/10.1186/1687-1812-2014-1
  20. J. Kumar, S. Vashistha, Coupled fixed point theorems in complex valued Gb-metric spaces, Adv. Fixed Point Theory 6 (2016), 341-351.
  21. A. Latifa, H. Isik, A.H. Ansari, Fixed points and functional equation problems via cyclic admissible generalized contractive type mappings, J. Nonlinear Sci. Appl. 9 (2016), 1129-1142. https://doi.org/10.22436/jnsa.009.03.40
  22. R. Miculescu, A. Mihail, New fixed point theorems for set-valued contractions in b-metric spaces, J. Fixed Point Theory Appl. 19 (2017), 2153-2163. https://doi.org/10.1007/s11784-016-0400-2
  23. P.K. Mishra, S. Sachdeva, S.K. Banerjee, Some fixed point theorems in b-metric space, Turkish Journal of Analysis and Number Theory 2 (2014), 19-22. https://doi.org/10.12691/tjant-2-1-5
  24. B. Moeini, H. Isik, H. Aydi, Related fixed point results via C*-class functions on C*-algebra-valued Gb-metric spaces, Carpathian Mathematical Publications 12 (2020), 94-106. https://doi.org/10.15330/cmp.12.1.94-106
  25. Z. Mustafa, B. Sims, A new approach to generalized metric spaces, Journal of Nonlinear and convex Anal. 7 (2006), 289-297.
  26. Z. Mustafa, H. Obiedat and F. Awawdeh, Some fixed point theorem for mappings on complete G-metric spaces, Fixed Point Theory and Appl. 2008 (2008), 1-12.
  27. Z. Mustafa, M. Khandagjy and W. Shatanawi, Fixed point results on complete G-metric Spaces, Studia Scientiarum Mathematicarum Hungarica 48 (2011), 304-319. https://doi.org/10.1556/SScMath.48.2011.3.1170
  28. Z. Mustafa, F. Awawdeh and W. Shatanawi, Fixed point theorem for expansive mappings in G-metric Spaces, Int. Journal of Contemp. Math. Sciences 5 (2010), 49-52.
  29. Z. Mustafa, H. Aydi and E. Karapinar, Mixed g-monotone property and quadruple fixed point theorems in partially ordered metric spaces, Fixed Point Theory Appl. 2012 (2012), 1-19. https://doi.org/10.1186/1687-1812-2012-1
  30. Z. Mustafa, J.R. Roshan, V. Parvaneh, Existence of tripled coincidence point in ordered Gb-metric spaces and applications to a system of integral equations, J. Inequal. Appl. 2013 (2013), 1-27. https://doi.org/10.1186/1029-242X-2013-1
  31. J.R. Roshan, N. Shobkolaei, S. Sedghi, V. Parvaneh, S. Radenovic, Common fixed point theorems for three maps in discontinuous Gb-metric spaces, Acta Math. Sci. Engl. Ser. 34 (2014), 1643-1654. https://doi.org/10.1016/S0252-9602(14)60110-7
  32. S. Sedghi, N. Shobkolaei, J.R. Roshan, W. Shatanawi, Coupled fixed point theorems in Gb-metric spaces, Mat. Vesnik 66 (2014), 190-201.
  33. W. Shatanawi, Some fixed point theorems in ordered G-metric spaces and applications, Abst. Appl. Anal. 2011 (2011), 1-11. https://doi.org/10.1155/2011/126205
  34. W. Shatanawi, A. Pitea, R. Lazovic, Contraction conditions using comparison functions on b-metric spaces, Fixed Point Theory Appl. 2014 (2014), 1-11. https://doi.org/10.1186/1687-1812-2014-1
  35. W. Sintunavarat, Nonlinear integral equations with new admissibility types in b-metric spaces, J. Fixed Point Theory Appl. 18 (2016), 397-416. https://doi.org/10.1007/s11784-015-0276-6
  36. O. Yamaod, W. Sintunavarat, Y.J. Cho, Common fixed point theorems for generalized cyclic contraction pairs in b-metric spaces with applications, Fixed Point Theory Appl. 2015 (2015), 1-18. https://doi.org/10.1186/1687-1812-2015-1