Research Article

A Note on The Equivalence of Some Metric and Non-Newtonian Metric Results

Volume: 7 December 19, 2017
EN

A Note on The Equivalence of Some Metric and Non-Newtonian Metric Results

Abstract

In this short note is on the equivalence between non-Newtonian metric
    (particularly multiplicative metric) and metric. We present a different
    proof the fact that the notion of a non-Newtonian metric space is not more
    general than that of a metric space. Also, we emphasize that a lot of fixed
    point results in the non-Newtonian metric setting can be directly obtained
    from their metric counterparts.

Keywords

References

  1. Abbas, M., Ali, B., Suleiman, Y.I., Common fixed points of locally contractive mappings in multiplicative metric spaces with application, Int. J. Math. Math. Sci., 2015, Art. ID 218683, 7 pp.
  2. Abbas, M., De la Sen, M., Nazir, T., Common fixed points of generalized rational type cocyclic mappings in multiplicative metric spaces, Discrete Dyn. Nat. Soc., 2015, Art. ID 532725, 10 pp.
  3. Binbaşıoğlu, D., Demiriz, S., Türkoğlu, D., Fixed points of non-Newtonian contraction mappings on non-Newtonian metric spaces, J. Fixed Point Theory Appl. 2015, doi: 10.1007/s11784-015-0271-y, 12 pp.
  4. Çakmak, A.F., Başar, F., Some new results on sequence spaces with respect to non-Newtonian calculus, J. Inequal. Appl. 2012, doi:10.1186/1029-242X-2012-228, 17 pp.
  5. Deshpande, B., Sheikh, S.A., Common fixed point theorems of Meir-Keeler type on multiplicative metric spaces, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math., 23(2016), no. 2, 131–143.
  6. Grossman, M., Katz, R., Non-Newtonian Calculus, Lee Press, Pigeon Cove, MA, 1972.
  7. Gu, F., Cho, Y.J., Common fixed point results for four maps satisfying \phi-contractive condition in multiplicative metric spaces, Fixed Point Theory Appl., 2015, 2015:165, 19 pp.
  8. He, X., Song, M., Chen, D., Common fixed points for weak commutative mappings on a multiplicative metric space, Fixed Point Theory Appl., 2014, 2014:48, 9 pp.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Bahri Turan
Gazi University
Türkiye

Cüneyt Çevik
Gazi University
Türkiye

Publication Date

December 19, 2017

Submission Date

September 28, 2017

Acceptance Date

November 9, 2017

Published in Issue

Year 2017 Volume: 7

APA
Turan, B., & Çevik, C. (2017). A Note on The Equivalence of Some Metric and Non-Newtonian Metric Results. Turkish Journal of Mathematics and Computer Science, 7, 56-58. https://izlik.org/JA87EB33MW
AMA
1.Turan B, Çevik C. A Note on The Equivalence of Some Metric and Non-Newtonian Metric Results. TJMCS. 2017;7:56-58. https://izlik.org/JA87EB33MW
Chicago
Turan, Bahri, and Cüneyt Çevik. 2017. “A Note on The Equivalence of Some Metric and Non-Newtonian Metric Results”. Turkish Journal of Mathematics and Computer Science 7 (December): 56-58. https://izlik.org/JA87EB33MW.
EndNote
Turan B, Çevik C (December 1, 2017) A Note on The Equivalence of Some Metric and Non-Newtonian Metric Results. Turkish Journal of Mathematics and Computer Science 7 56–58.
IEEE
[1]B. Turan and C. Çevik, “A Note on The Equivalence of Some Metric and Non-Newtonian Metric Results”, TJMCS, vol. 7, pp. 56–58, Dec. 2017, [Online]. Available: https://izlik.org/JA87EB33MW
ISNAD
Turan, Bahri - Çevik, Cüneyt. “A Note on The Equivalence of Some Metric and Non-Newtonian Metric Results”. Turkish Journal of Mathematics and Computer Science 7 (December 1, 2017): 56-58. https://izlik.org/JA87EB33MW.
JAMA
1.Turan B, Çevik C. A Note on The Equivalence of Some Metric and Non-Newtonian Metric Results. TJMCS. 2017;7:56–58.
MLA
Turan, Bahri, and Cüneyt Çevik. “A Note on The Equivalence of Some Metric and Non-Newtonian Metric Results”. Turkish Journal of Mathematics and Computer Science, vol. 7, Dec. 2017, pp. 56-58, https://izlik.org/JA87EB33MW.
Vancouver
1.Bahri Turan, Cüneyt Çevik. A Note on The Equivalence of Some Metric and Non-Newtonian Metric Results. TJMCS [Internet]. 2017 Dec. 1;7:56-8. Available from: https://izlik.org/JA87EB33MW