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Yeni Bir Genelleştirilmiş Normlu Uzay: A-Normlu Uzaylar

Year 2022, Volume: 10 Issue: 2, 748 - 754, 30.04.2022
https://doi.org/10.29130/dubited.984464

Abstract

Bu çalışmada, normlu uzayların bir genelleştirmesi olarak A-normlu uzay kavramı tanımlandı ve bu yeni uzayın bazı temel özellikleri incelendi. Ayrıca A-metrik uzay ile A-normlu uzay arasındaki ilişki araştırıldı.

References

  • [1]Fréchet,M. M., "Sur quelques points du calcul fonctionnel," Rendiconti del Circolo Matematico di Palermo (1884-1940), vol. 22, no. 1, pp. 1-72, 1906.
  • [2]S. Gähler, "2Metriche raume und ihre topologische strukture,"Math. Nachr. vol. 26, pp. 115–148, 1963.
  • [3]K. S. Ha, Y. J. Cho and A. White, "Strictly convex and strictly 2-convex 2-normed spaces," Math. Jpn., vol. 33, no. 3, pp. 375–384, 1988.
  • [4]B. C. Dhage, "Generalized metric spaces and mapping with fixed point,"Bull. Cal.Math. Soc.,vol. 84, pp. 329–336, 1992.
  • [5]Z. Mustafa and B. Sims, "Some remarks concerning metric spaces," inInternational Conferences on Fixed Point Theory and Application,Valencia, Spain, 2003, pp. 189-198.
  • [6]Z. Mustafa, and B. Sims, "A new approach to generalized metric spaces,"Journal of Nonlinear and Convex Analysis, vol. 7, no.2, pp. 289-297, 2006.
  • [7]S. Sedghi,N. Shobeand A. Aliouche, "A generalization of fixed point theorem in metric spaces,"Matematicki Vesnik, vol. 64, no. 3, pp. 258-266, 2012.
  • [8]M. Abbas, B. Ali and Y. I. Suleiman, "Generalized coupled common fixed point results in partially ordered A-metric spaces," Fixed Point Theory and Applications, vol. 2015, no. 1, pp. 1-24, 2015.
  • [9]S. Gähler, "Lineare 2-normierte räume,"Math. Nachr. vol. 28,pp. 1–43, 1964.
  • [10]K. A. Khan, "Generalized normed spaces and fixed point theorems," Journal of Mathematics and Computer Science, vol. 13, pp. 157-167, 2014.
  • [11]A. Mutlu, U. Gürdal and K. Özkan, "A New Approach to G-Normed Spaces: Functionally Generalized Normed Spaces," Celal Bayar University Journal of Science, vol. 14, pp. 1-12, 2018.
  • [12]N. Taş and N. Özgür, "A New Generalization of Rhoades' Condition,"2021, arXiv:2105.13129.
  • [13]G. Zaim Erçınar, "Sabit Noktaların Bazı Geometrik Özellikleri," Ph.D. dissertation, Dept. Mathematics, Osmangazi Üniversitesi,Eskişehir, Türkiye, 2020.

A New Generalization of Normed Spaces: A-Normed Spaces

Year 2022, Volume: 10 Issue: 2, 748 - 754, 30.04.2022
https://doi.org/10.29130/dubited.984464

Abstract

In this study, the concept of A-normed space as a generalization of normed spaces is defined and some basic properties of this new space are examined. In addition, the relationship between A-metric space and A-normed space is investigated.

References

  • [1]Fréchet,M. M., "Sur quelques points du calcul fonctionnel," Rendiconti del Circolo Matematico di Palermo (1884-1940), vol. 22, no. 1, pp. 1-72, 1906.
  • [2]S. Gähler, "2Metriche raume und ihre topologische strukture,"Math. Nachr. vol. 26, pp. 115–148, 1963.
  • [3]K. S. Ha, Y. J. Cho and A. White, "Strictly convex and strictly 2-convex 2-normed spaces," Math. Jpn., vol. 33, no. 3, pp. 375–384, 1988.
  • [4]B. C. Dhage, "Generalized metric spaces and mapping with fixed point,"Bull. Cal.Math. Soc.,vol. 84, pp. 329–336, 1992.
  • [5]Z. Mustafa and B. Sims, "Some remarks concerning metric spaces," inInternational Conferences on Fixed Point Theory and Application,Valencia, Spain, 2003, pp. 189-198.
  • [6]Z. Mustafa, and B. Sims, "A new approach to generalized metric spaces,"Journal of Nonlinear and Convex Analysis, vol. 7, no.2, pp. 289-297, 2006.
  • [7]S. Sedghi,N. Shobeand A. Aliouche, "A generalization of fixed point theorem in metric spaces,"Matematicki Vesnik, vol. 64, no. 3, pp. 258-266, 2012.
  • [8]M. Abbas, B. Ali and Y. I. Suleiman, "Generalized coupled common fixed point results in partially ordered A-metric spaces," Fixed Point Theory and Applications, vol. 2015, no. 1, pp. 1-24, 2015.
  • [9]S. Gähler, "Lineare 2-normierte räume,"Math. Nachr. vol. 28,pp. 1–43, 1964.
  • [10]K. A. Khan, "Generalized normed spaces and fixed point theorems," Journal of Mathematics and Computer Science, vol. 13, pp. 157-167, 2014.
  • [11]A. Mutlu, U. Gürdal and K. Özkan, "A New Approach to G-Normed Spaces: Functionally Generalized Normed Spaces," Celal Bayar University Journal of Science, vol. 14, pp. 1-12, 2018.
  • [12]N. Taş and N. Özgür, "A New Generalization of Rhoades' Condition,"2021, arXiv:2105.13129.
  • [13]G. Zaim Erçınar, "Sabit Noktaların Bazı Geometrik Özellikleri," Ph.D. dissertation, Dept. Mathematics, Osmangazi Üniversitesi,Eskişehir, Türkiye, 2020.
There are 13 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Elif Kaplan 0000-0002-7620-3387

Publication Date April 30, 2022
Published in Issue Year 2022 Volume: 10 Issue: 2

Cite

APA Kaplan, E. (2022). Yeni Bir Genelleştirilmiş Normlu Uzay: A-Normlu Uzaylar. Duzce University Journal of Science and Technology, 10(2), 748-754. https://doi.org/10.29130/dubited.984464
AMA Kaplan E. Yeni Bir Genelleştirilmiş Normlu Uzay: A-Normlu Uzaylar. DUBİTED. April 2022;10(2):748-754. doi:10.29130/dubited.984464
Chicago Kaplan, Elif. “Yeni Bir Genelleştirilmiş Normlu Uzay: A-Normlu Uzaylar”. Duzce University Journal of Science and Technology 10, no. 2 (April 2022): 748-54. https://doi.org/10.29130/dubited.984464.
EndNote Kaplan E (April 1, 2022) Yeni Bir Genelleştirilmiş Normlu Uzay: A-Normlu Uzaylar. Duzce University Journal of Science and Technology 10 2 748–754.
IEEE E. Kaplan, “Yeni Bir Genelleştirilmiş Normlu Uzay: A-Normlu Uzaylar”, DUBİTED, vol. 10, no. 2, pp. 748–754, 2022, doi: 10.29130/dubited.984464.
ISNAD Kaplan, Elif. “Yeni Bir Genelleştirilmiş Normlu Uzay: A-Normlu Uzaylar”. Duzce University Journal of Science and Technology 10/2 (April 2022), 748-754. https://doi.org/10.29130/dubited.984464.
JAMA Kaplan E. Yeni Bir Genelleştirilmiş Normlu Uzay: A-Normlu Uzaylar. DUBİTED. 2022;10:748–754.
MLA Kaplan, Elif. “Yeni Bir Genelleştirilmiş Normlu Uzay: A-Normlu Uzaylar”. Duzce University Journal of Science and Technology, vol. 10, no. 2, 2022, pp. 748-54, doi:10.29130/dubited.984464.
Vancouver Kaplan E. Yeni Bir Genelleştirilmiş Normlu Uzay: A-Normlu Uzaylar. DUBİTED. 2022;10(2):748-54.