Dissemination of Suzuki Contraction Theorem in a Metric Space

Abstract

A novel and robust extension of the traditional Banach contraction theorem is the Suzuki contraction theorem [47]. One of the most prominent statements in the field of metric fixed-point is this theorem. A comprehensive overview of the Suzuki contraction theorem's developments over the past 15 years is covered in this study. This paper offers an explanation of the literature that advances the Suzuki contraction theorem by improving, extending, and generalizing it to metric spaces.

Country : India

1 Manju Devi2 Raj Kamal

  1. Department of Mathematics, Dr. B. R. Ambedkar Government College, Jagdishpura, Kaithal, 136027, India
  2. Department of Mathematics, Government College, Jind, 126102, India

IRJIET, Volume 10, Issue 1, January 2026 pp. 51-65

doi.org/10.47001/IRJIET/2026.101007

References

  1. M. Abbas, B. Ali and S. N. Mishra, Fixed points of multivalued SuzukiZamfirescu-(f; g) contraction mappings, MatematickiVesnik (2012), 1–15.
  2. M. Abbas, B. Ali and C. Vetro, A Suzuki type fixed point theorem for a generalized multivalued mapping on partial Hausdorff metric spaces, Topology Appl. 160 (2013), 553–563.
  3. M. Akkouchi, A Meir-Keeler type common fixed point theorem for four maps, Opuscula Math. 31(1) (2011), 5–14.
  4. S. M. A. Aleomraninejad, Sh. Rezapour and N. Shahzad, On fixed point generalizations of Suzuki’s method, Appl. Math. Letters 24 (2011), 1037–1040.
  5. I.Altun and A. Erduran, A Suzuki type fixed-point theorem, Internat. J. Math. Math. Sci. (2011), 1-9.
  6. S. Banach, Sur les operations dans les ensembles abstraitsetleur application aur equations integrals, Fund. Math., 3 (1922), 133-181.
  7. R.K.Bose, Some Suzuki type fixed point theorems for generalized contractive multifunctions, Int. J Pure Appl Math. 84(1), (2013), 13-27.
  8. Lj. B. Ćirić, Fixed points for generalized multivalued contractions, Mat. Vsenik. 9 (1972), 265-272.
  9. Lj. B. Ciric, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc. 45 (2) (1974), 267–273.
  10. N. Chandra, B. Joshi and M.C. Joshi, Generalized fixed point theorems on metric spaces, Mathematica Moravica, Vol. 26, No.2, (2022), 85-101.
  11. B.Đamjanović and Đ.Đorić, Multivalued generalizations of the Kannan fixed point theorem, Filomat 25:1 (2011), 125-131.
  12. S. Dhompongsa and H. Yingtaweesittikul, Fixed points for multivalued mappings and the metric completeness, Fixed Point Theory Appl. 2009(2009), 1-15.
  13. D. Dori`c, Common fixed point for generalized (φ, ϕ) - weak contraction, Appl. Math. Letters 22 (2009), 1896–1900.
  14. D.Dorić and R.Lazović, Some Suzuki-type fixed point theorems for generalized multivalued mappings and applications, Fixed Point Theory Appl. 2011(2011), 1-13.
  15. P. N. Dutta and B. S. Choudhary, A generalization of contraction principle in metric spaces, Fixed Point Theory Appl. 2008 (2008), 1–8.
  16. M. Edelstein, An extension of Banach’s contraction principle, Proc. Amer. Math. Soc. 12 (1961), 7–10.
  17. Y. Enjouji, M. Nakanishi and T. Suzuki, A generalization of Kannan’s fixed point theorem, Fixed Point Theory Appl. 2009 (2009), 1–10.
  18. A.Granas and J. Dugundji, Fixed point theory, Springer Verlag, 2003.
  19. G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly 83 (1976), 261-263.
  20. R. Kamal, R.Chugh, S. L. Singh and S. N. Mishra, New common fixed point theorems for multivalued maps, Applied General Topology, 15(2), (2014), 111-119.
  21. R. Kannan, Some results on fixed points, Bull. Cal. Math. Soc. 60 (1968), 71-76.
  22. E. Karapinar, Interpolative Kannan-Meir-Keeler type contraction, Advances in the theory of Nonlinear Analysis and its Applications 5, (2021), No-4, 611-614.
  23. E. Karapinar, Revisiting the Kannan type contractions via Interpolation, Advances in the theory of Nonlinear Analysis and its Applications 2, (2018), No-2, 85-87.
  24. E. Karapinar, O. Alqahtani and H. Aydi, On interpolative Hardy-Rogers type contractions, Symmetry, 11(1), 8, (2018), 1-7.
  25. M. Kikkawa and T. Suzuki, Some similarity between contractions and Kannan Mappings, Fixed Point Theory Appl. 2008(2008), 1-8.
  26. M.Kikkawa and T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal. 69(9) (2008), 2942– 2949.
  27. M.Kikkawa and T. Suzuki, Some Notes on fixed point theorems with constants, Bull. Kyushu Inst. Tech. Pure Appl. Math. No. 56 (2009), 11-18.
  28. C.Kulshrestha, Single–Valued Mappings, Multivalued Mappings and Fixed Points Theorems in Metric Spaces, D. Phil. Thesis, Garhwal Univ. Srinagar, 1983.
  29. A.Meir and E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl. 28(1969), 326-329.
  30. G. Mot and A. Petrusel, Fixed point theory for a new type of contractive multivalued operators, Nonlinear Anal .70(2009), 3371-3377.
  31. S. B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475-488.
  32. S. B. Nadler Jr., Hyperspaces of Sets, Marcel Dekker, New York, 1978.
  33. R. P. Pant, Meir-Keeler type fixed point theorems and dynamics of functions, Demonstratio Math. 35 (2003), 199–206.
  34. R. P. Pant and K. Jha, A generalization of Meir-Keeler type common fixed point theorem for four mappings, Indian J. Natur. Phys. Sci. 16(1-2) (2002), 77–84.
  35. R. Pant and S.N. Mishra, Stability results for Suzuki contractions with an application to initial value problems, Filomat, 32(9), (2018), 3297-3304.
  36. S. Park and B. E. Rhoades, Meir-Keeler type contractive conditions, Math. Japon. 26 (1981), 13–20.
  37. O.Popescu, Two fixed point theorems for generalized contractions with constants in complete metric space, Cent. Eur. J. Math. 7(3) (2009), 529–538.
  38. K.P.R.Rao, K.R.K. Rao and V.C.C. Raju, A Suzuki type unique common coupled fixed point theorem in metric spaces, Int. J. Inn. Res. In Sci, Eng. And Tech, 2(10), (2013), 5187-5192.
  39. B. E. Rhoades, A comparison of various definitions of contractive mappings, Tran. Amer. Math. Soc. 226 (1977), 257-290.
  40. S. L. Singh, R.Chugh and R. Kamal, Suzuki type common fixed point theorems and applications, Fixed Point Theory, 14(2), (2013), 497-506.
  41. S. L. Singh and S. N. Mishra, Coincidence theorems for certain classes of hybrid contractions, Fixed Point Theory Appl. 2010 (2010), 1-14.
  42. S. L. Singh and S. N. Mishra, Remarks on recent fixed point theorems, Fixed Point Theory Appl. 2010(2010), 1-18.
  43. S. L. Singh and S. N. Mishra, Fixed point theorems for single-valued and multi-valued maps. Nonlinear Anal. 74(6) (2011), 2243-2248.
  44. S. L. Singh, R. Kamal and M. De La Sen, Coincidence and common fixed point theorems for Suzuki type hybrid contractions and applications, Fixed Point Theory Appl., (2014), 147.
  45. S. L. Singh, R. Kamal , M. De La Sen and R. Chugh, A new type of coincidence and common fixed point theorem with applications, Abstract and Applied Analysis, (2014), 1-11.
  46. S. L. Singh, S. N. Mishra, R. Chugh and R. Kamal, General common fixed point theorems and applications, J. Appl. Math. (2012), 1-14.
  47. T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136(5) (2008), 1861–1869.
  48. T. Suzuki, Fixed point theorems and convergence theorems for some generalized non-expansive mappings, J. Math. Anal. Appl. 340(2008), 1088-1095.
  49. T. Suzuki and M.Kikkawa, Some remarks on a recent generalization of the Banach contraction principle, Proceedings of the Eighth International Conference on Fixed Point Theory and Applications, Yokohama Publishers, (2008), 151-161.
  50. S.S. Yesilkaya, On interpolative Hardy-Rogers contractive of Suzuki type mappings, Topol. Algebra Appl. 9(2021), 13-19.