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

Yıl 2018, Cilt: 1 Sayı: 3, 153 - 157, 30.12.2018
https://doi.org/10.33187/jmsm.416632

Öz

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.

Kaynakça

  • [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.
Yıl 2018, Cilt: 1 Sayı: 3, 153 - 157, 30.12.2018
https://doi.org/10.33187/jmsm.416632

Öz

Kaynakça

  • [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.
Toplam 32 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Memudu Olatinwo

Yayımlanma Tarihi 30 Aralık 2018
Gönderilme Tarihi 18 Nisan 2018
Kabul Tarihi 14 Eylül 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 1 Sayı: 3

Kaynak Göster

APA Olatinwo, M. (2018). A New Generalization of Non-Unique Fixed Point Theorems of $\acute{C}$iri$\acute{c}$ for Akram-Zafar-Siddiqui Type Contraction. Journal of Mathematical Sciences and Modelling, 1(3), 153-157. https://doi.org/10.33187/jmsm.416632
AMA Olatinwo M. A New Generalization of Non-Unique Fixed Point Theorems of $\acute{C}$iri$\acute{c}$ for Akram-Zafar-Siddiqui Type Contraction. Journal of Mathematical Sciences and Modelling. Aralık 2018;1(3):153-157. doi:10.33187/jmsm.416632
Chicago Olatinwo, Memudu. “A New Generalization of Non-Unique Fixed Point Theorems of $\acute{C}$iri$\acute{c}$ for Akram-Zafar-Siddiqui Type Contraction”. Journal of Mathematical Sciences and Modelling 1, sy. 3 (Aralık 2018): 153-57. https://doi.org/10.33187/jmsm.416632.
EndNote Olatinwo M (01 Aralık 2018) A New Generalization of Non-Unique Fixed Point Theorems of $\acute{C}$iri$\acute{c}$ for Akram-Zafar-Siddiqui Type Contraction. Journal of Mathematical Sciences and Modelling 1 3 153–157.
IEEE M. Olatinwo, “A New Generalization of Non-Unique Fixed Point Theorems of $\acute{C}$iri$\acute{c}$ for Akram-Zafar-Siddiqui Type Contraction”, Journal of Mathematical Sciences and Modelling, c. 1, sy. 3, ss. 153–157, 2018, doi: 10.33187/jmsm.416632.
ISNAD Olatinwo, Memudu. “A New Generalization of Non-Unique Fixed Point Theorems of $\acute{C}$iri$\acute{c}$ for Akram-Zafar-Siddiqui Type Contraction”. Journal of Mathematical Sciences and Modelling 1/3 (Aralık 2018), 153-157. https://doi.org/10.33187/jmsm.416632.
JAMA Olatinwo M. A New Generalization of Non-Unique Fixed Point Theorems of $\acute{C}$iri$\acute{c}$ for Akram-Zafar-Siddiqui Type Contraction. Journal of Mathematical Sciences and Modelling. 2018;1:153–157.
MLA Olatinwo, Memudu. “A New Generalization of Non-Unique Fixed Point Theorems of $\acute{C}$iri$\acute{c}$ for Akram-Zafar-Siddiqui Type Contraction”. Journal of Mathematical Sciences and Modelling, c. 1, sy. 3, 2018, ss. 153-7, doi:10.33187/jmsm.416632.
Vancouver Olatinwo M. A New Generalization of Non-Unique Fixed Point Theorems of $\acute{C}$iri$\acute{c}$ for Akram-Zafar-Siddiqui Type Contraction. Journal of Mathematical Sciences and Modelling. 2018;1(3):153-7.

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