Yeni Bir Genelleştirilmiş Normlu Uzay: A-Normlu Uzaylar

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.

Anahtar Kelimeler:

A-metrik uzay, Genelleştirilmiş normlu uzay, A-normlu uzay

A New Generalization of Normed Spaces: A-Normed Spaces

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.

Keywords:

A-metric space, Generalized normed space, A-normed space,

PDF

___

[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.