Pata-Type Fixed Point Results in bv(s)-Metric Spaces

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Fangyuan Dong, Peisheng Ji, Xiaohui Wang, Pata-Type Fixed Point Results in bv(s)-Metric Spaces, Int. J. Anal. Appl., 17 (3) (2019), 342-360.

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Fangyuan Dong, Peisheng Ji, Xiaohui Wang

Abstract

The aim of this is to study fixed point theorems in bν(s)-metric spaces under the Pata-type conditions. As consequences, we establish common fixed point results of Pata-type for two maps in bν(s)- metric spaces.

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References

  1. M. Abbas, N. Saleem and M. De la Sen, Optimal coincidence point results in partially ordered non-Archimedean fuzzy metric spaces, Fixed Point Theory Appl. 2016(2016), Art. ID 44.
  2. J. Ahmad, M. Arshad and C. Vetro, On a theorem of Khan in a Generalized Metric Space, Int. J. Anal. 2013(2013), Art. ID 852727.
  3. Arslan Hojat Ansari and Anchalee Kaewcharoen, C-class functions and fixed point theorems for generalized α-η-ψ-φ-Fcontraction type mappings in α-η-complete metric spaces, J. Nonlinear Sci. Appl. 9(2016), 4177-4190.
  4. I.A. Bakhtin, The contraction mapping principle in quasi-metric space
  5. [in Russian], Funk.An. Ulianowsk Gos. Ped. Inst. 30(1989), 26-37.
  6. S. Balasubramanian, A Pata-type fixed point theorem, Math. Sci. 8(2014), 65-69.
  7. S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrals, Fundam. Math. 3(1922), 133-181.
  8. A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen 57(2000), 31-37.
  9. S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inf. Univ. Ostrav. 1(1993), 5-11.
  10. M. Eshaghi, S.Mohseni, M.R. Delavar, M. De La Sen, G. H. Kim and A. Arian, Pata contractions and coupled type fixed points, Fixed Point Theory Appl. 2014(2014), Art. ID 130.
  11. K. Fan, Extensions of two fixed point Theorems of F. E. Browder, Math. Z. 112(1969), 234-240.
  12. B. Fisher, On a theorem of Khan, Riv. Math. Univ. Parma. 4(1978), 135-137.
  13. R. George, S. Radenovic, K.P. Reshma and S. Shukla, Rectangular b-metric spaces and contraction principle, J. Nonlinear Sci. Appl. 8(2016), 1005-1013.
  14. R. H. Haghi, S. Rezapour and N. Shahzad, Some fixed point generalizations are not real generalizations, Nonlinear Anal., Model. Control 74(2011), 1799-1803.
  15. Z. Kadelburg and S. Radenovic, Fixed point and tripled fixed point theorems under Pata-type conditions in ordered metric space, Int. J. Anal. Appl. 6(2014),113-122.
  16. Z. Kadelburg and S. Radenovic, Fixed point theorems for Pata-type maps in ordered metric space, J. Egypt. Math. Soc. 24(2016), 77-82.
  17. Z. Kadelburg and S. Radenovic, A note on Pata-type cyclic contractions, Sarajevo J. Math. 11(2015), 235-245.
  18. Z. Kadelburg and S. Radenovic, Pata-type common fixed point results in b-metric and b-rectangular metric spaces, J. Nonlinear Sci. Appl. 8(2015), 944-954.
  19. M. S. Khan, M. Swaleh and S. Sessa, Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc. 30(1984), 1-9.
  20. W. A. Kirk and N. Shahzad, Generalized metrics and Caristis theorem, Fixed Point Theory Appl. 2013(2013), Art. ID 129.
  21. Ma Zhenhua, Jiang Lining and Sun Hongkai, C*-algebra-valued metric spaces and related fixed point theorems, Fixed Point Theory Appl. 2014(2014), Art. ID 206.
  22. Z.D. Mitrovic and S. Radenovic, The Banach and Reich contractions in bν(s)-metric spaces, J. Fixed Point Theory Appl. 19(2017), 3087-3905.
  23. D.D. Mitrovic, and S. Radenovic, A common fixed point theorem of Jungck in rectangular b-metric spaces, Acta Math. Hungar. 153(2017), 401-407.
  24. V. Pata, A fixed point theorem in metric spaces, J. Fixed Point Theory Appl. 10(2011), 299-305.
  25. H. Piri, S. Rahrovi and P. Kumam, Khan type fixed point theorems in a generalized metric space, J. Math. Computer Sci. 16(2016), 211-217.
  26. M. Rangamma and P. M. Reddy, A common fixed point theorem for T-contractions on generalized cone b-metric spaces, Commun. Korean Math. Soc. 32(2017), 65-74.
  27. Z. Raza, N. Saleem and M. Abbas, Optimal coincidence points of proximal quasi-contraction mappings in non-Archimedean fuzzy metric spaces, J. Nonlinear Sci. Appl. 9(2016), 3787-3801.
  28. V. L. Rosa and P. Vetro, Common fixed points for α - ψ - φ-contractionseneralized in g metric spaces, Nonlinear Anal., Model. Control 19(2014), 43-54.
  29. J. R. Roshan, Vahid Parvaneh, Z. Kadelburg and N. Hussain, New fixed point results in b-rectangular metric spaces, Nonlinear Anal., Model. Control 21(2006),614-634.
  30. N. Saleem, M. Abbas and Z. Raza, Optimal coincidence best approximation solution in non-Archimedean Fuzzy Metric Spaces, Iran. J. Fuzzy Syst. 13(2016), 113-124.
  31. N. Saleem, B. Ali, M. Abbas and Z. Raza, Fixed points of Suzuki type generalized multivalued mappings in fuzzy metric spaces with applications, Fixed Point Theory Appl. 2015(2015), Art. ID 36.
  32. B. Samet, Discussion on 'a fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces' by Branciari, Publ. Math. Debrecen, 76(2010), 493-494.
  33. I. R. Sarma, J. M. Rao and S. S. Rao, Contractions over generalized metric spaces, J. Nonlinear Sci. Appl. 2(2009), 180-182.
  34. Shen Congcong, Jiang Lining and Ma Zhenhua, C*-Algebra-Valued G-Metric Spaces and Related Fixed- Point Theorems, J. Function Spaces 2018(2018), Article ID 3257189.
  35. Vahid Parvaneh, Nawab Hussain and Zoran Kadelburg, Generalized Wardowski type fixed point theorems via α-admissable F G-contractions in b-metric spaces, Acta Math. Sci. 5(2016), 1445-1456.
  36. T.Suzuki, generalized metric spaces do not have the compatible topology, Abstr. Appl. Anal. 2014(2014), Art. ID 458098.
  37. Wang Liguang, Liu Bo and Bai Ran, Stability of a Mixed Type Functional Equation on Multi-Banach Spaces, A Fixed Point Approach, Fixed Point Theory Appl. 2010(2010), Art. ID 283827.