A New Generalization of Non-Unique Fixed Point Theorems of $\acute{C}$iri$\acute{c}$ for Akram-Zafar-Siddiqui Type Contraction

A New Generalization of Non-Unique Fixed Point Theorems of $\acute{C}$iri$\acute{c}$ for Akram-Zafar-Siddiqui Type Contraction

In this article, we establish some fixed point theorems of $\acute{C}$iri$\acute{c}$'s type for Akram-Zafar-Siddiqui type contractive mappings having non-unique fixed points. Our results generalize, extend and improve several ones in the literature.

___

  • [1] Lj. B. Ciric, On contraction type mappings, Math. Balkanica, 1 (1971), 52-57.
  • [2] Lj. B. Ciric, Some Recent Results in Metrical Fixed Point Theory, University of Belgrade, 2003.
  • [3] Lj. B. Ciric, On some maps with a nonunique fixed point, Publ. Inst. Math., 17 (31) (1974), 52-58.
  • [4] S. Banach, Sur les operations dans les ensembles abstraits et leur applications aux equations integrales, Fund. Math., 3 (1922), 133-181.
  • [5] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 10 (1968), 71-76.
  • [6] S. K. Chatterjea, Fixed-point theorems, C. R. Acad. Bulgare Sci., 10 (1972), 727-730.
  • [7] T. Zamfirescu, Fix point theorems in metric spaces, Arch. Math., 23 (1972), 292-298.
  • [8] M. Akram, A. A. Zafar, A. A. Siddiqui, A general class of contractions: A?contractions, Novi Sad J. Math., 38(1) (2008), 25-33.
  • [9] M. O. Olatinwo, Some new fixed point theorems in complete metric spaces, Creat. Math. Inf. 21(2) (2012), 189-196.
  • [10] M. O. Olatinwo, Non-unique fixed point theorems of ´Ciri ´ c’s type for rational hybrid contractions, Nanjing Univ. J. Math. Biquarterly, 31(2) (2014), 140-149.
  • [11] M. O. Olatinwo, Some Ciric’s type non-unique fixed point theorems and rational type contractive conditions, Kochi J. Math., 10 (2015), 1-9.
  • [12] M. O. Olatinwo, Some non-unique fixed point theorems of Ciric’s type using rational type contractive conditions, Georgian Math. J., 24(3) (2017), 455-461.
  • [13] J. Achari, On Ciric’s nonunique fixed points, Mat. Vesnik, 13(28) (1976), 255-257.
  • [14] J. Achari, Results on nonunique fixed points, Publ. Inst. Math. Nouvelle Serie, 26(40) (1979), 5-9.
  • [15] J. Achari, On the generalization of Pachpatte’s nonunique fixed point theorem, Indian J. Pure Appl. Math., 13(3) (1982), 299-302.
  • [16] Lj. B. Ciric, N. Jotic, A further extension of maps with nonunique fixed points, Mat. Vesnik, 50 (1998), 1-4.
  • [17] E. Karapinar, Some nonunique fixed point theorems of Ciric type on cone metric spaces, Abstr. Appl. Anal., 2010, Article ID 123094, 14 pages.
  • [18] B. G. Pachpatte, On Ciric type maps with a non-unique fixed point, Indian J. Pure Appl. Math., 10(8) (1979), 1039-1043.
  • [19] M. G. Maia, Un’osservazione sulle contrazioni metriche, Rend. Sem. Mat. Univ. Padova, 40 (1968), 139-143.
  • [20] M. O. Olatinwo, Non-unique fixed point theorems of Achari and Ciric-Jotic types for hybrid contractions, J. Adv. Math. Stud., 9(2) (2016), 226-234.
  • [21] R. P. Agarwal, M. Meehan, D. O’Regan, Fixed Point Theory and Applications, Cambridge University Press, 2004.
  • [22] T. Basu, Extension of Ciric’s fixed point theorem in a uniform space, Ranchi Univ. Math. J., 11 (1980), 109-115.
  • [23] V. Berinde, Iterative Approximation of Fixed Points, Editura Efemeride, 2002.
  • [24] V. Berinde, Approximating Fixed Points of Weak Contractions using Picard Iteration, Nonlinear Anal. Forum, 9(1) (2004), 43-53.
  • [25] V. Berinde, Iterative Approximation of Fixed Points, Springer-Verlag Berlin Heidelberg (2007).
  • [26] D. S. Jaggi, Some unique fixed point theorems, Indian J. Pure Appl. Math., 8(2) (1977), 223-230.
  • [27] M. A. Khamsi, W. A. Kirk, An Introduction to Metric Spaces and Fixed Point Theory, John Wiley & Sons, Inc. (2001).
  • [28] A. R. Khan, V. Kumar, N. Hussain, Analytical and numerical treatment of Jungck-type iterative scheme, Appl. Math. Comput., 231 (2014), 521-535.
  • [29] M. O. Olatinwo, Some stability and convergence results for Picard, Mann, Ishikawa and Jungck type iterative algorithms for Akram-Zafar-Siddiqui type contraction mappings, Nonlinear Anal. Forum, 21(1) (2016), 65-75.
  • [30] I. A. Rus, Generalized Contractions and Applications, Cluj Univ. Press, Cluj Napoca, 2001.
  • [31] I. A. Rus, A. Petrusel, G. Petrusel; Fixed Point Theory, 1950-2000, Romanian contributions, House of the Book of Science, Cluj Napoca, 2002.
  • [32] E. Zeidler, Non-Linear Functional Analysis and Its Applications-Fixed Point Theorems, Springer-Verlag, New York, Inc., 1986.
Journal of Mathematical Sciences and Modelling-Cover
  • ISSN: 2636-8692
  • Yayın Aralığı: Yılda 3 Sayı
  • Başlangıç: 2018
  • Yayıncı: Mahmut AKYİĞİT