Year 2020, Volume 49 , Issue 3, Pages 1076 - 1083 2020-06-02

In the present paper, we introduce the concept of $\mathcal{F}$-modular, which is a generalization of the modular notion. Moreover, we introduce a $K_p$-modular and $K$-modular, and then compare these concepts together. Finally, we give a characterization of $\mathcal{F}$-modulars.
Modular space, K-modular space, F-modular space
  • [1] A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen 57, 31-37, 2000.
  • [2] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Univ. Ostrav. 1 (1), 511, 1993.
  • [3] R. Fagin, R. Kumar and D. Sivakumar, Comparing top k lists, SIAM J. Discrete Math. 17 (1), 134-160, 2003.
  • [4] V.S. G¨ahler, 2-metrische R¨aume und ihre topologische struktur, Math. Nachr. 26, 115-118, 1963/1964.
  • [5] M. Jleli and B. Samet, A generalized metric space and related fixed point theorems, Fixed Point Theory Appl. 2015, 14 pages, 2015.
  • [6] M. Jleli and B. Samet, On a new generalization of metric spaces, Fixed Point Theory Appl. 20 (3), 20 pages, 2018.
  • [7] R. Kopperman and H. Pajoohesh, Generalizations of metrics and partial metrics, Hacet. J. Math. Stat. 46 (1), 9-14, 2017.
  • [8] S. Koshi and T. Shimogaki, On F–norms of quasi–modular spaces, J. Fac. Sci. Hokkaido Univ. Ser. I. 15 (3), 202-218, 1961.
  • [9] M.A. Krasnoselskii and Y.B. Rutickii, Convex functions and Orlicz spaces (in Russian), Fizmatgiz, Moskva, 1958; Translated by L.F. Boron, Noordhoff, Groningen, 1961.
  • [10] W.A. Luxemburg, Banach function spaces, Ph. D. Thesis, Delft University of Technology, Delft, The Netherlands, 1959.
  • [11] L. Maligranda, Orlicz Spaces and Interpolation, in: Seminars in Math. 5, Univ. of Campinas, Brazil, 1989.
  • [12] S.G. Matthews, Partial metric topology, Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci. 728, 183-197, 1994.
  • [13] J. Musielak, Orlicz Spaces and Modular Spaces, in: Lecture Notes in Math. 1034, Springer-Verlag, Berlin, 1983.
  • [14] Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2), 289-297, 2006.
  • [15] H. Nakano, Modulared Semi-Ordered Linear Spaces, in: Tokyo Math. Book Ser. 1, Maruzen Co., Tokyo, 1950.
  • [16] W. Orlicz, Collected Papers, Vols. I, II, PWN, Warszawa, 1988.
  • [17] T.L. Shateri, C∗-algebra-valued modular spaces and fixed point theorems, J. Fixed Point Theory Appl. 19 (2), 1551-1560, 2017.
  • [18] S. Yamamuro, On conjugate spaces of Nakano spaces, Trans. Amer. Math. Soc. 90, 291-311, 1959.
Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0002-5181-6558
Author: Tayebe LAL SHATERİ (Primary Author)
Institution: Hakim Sabzevari University
Country: Iran


Dates

Publication Date : June 2, 2020

Bibtex @research article { hujms531654, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1076 - 1083}, doi = {10.15672/hujms.531654}, title = {New generalizations of Modular spaces}, key = {cite}, author = {Lal Shateri̇, Tayebe} }
APA Lal Shateri̇, T . (2020). New generalizations of Modular spaces . Hacettepe Journal of Mathematics and Statistics , 49 (3) , 1076-1083 . DOI: 10.15672/hujms.531654
MLA Lal Shateri̇, T . "New generalizations of Modular spaces" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1076-1083 <https://dergipark.org.tr/en/pub/hujms/issue/54699/531654>
Chicago Lal Shateri̇, T . "New generalizations of Modular spaces". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1076-1083
RIS TY - JOUR T1 - New generalizations of Modular spaces AU - Tayebe Lal Shateri̇ Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.531654 DO - 10.15672/hujms.531654 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1076 EP - 1083 VL - 49 IS - 3 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.531654 UR - https://doi.org/10.15672/hujms.531654 Y2 - 2019 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics New generalizations of Modular spaces %A Tayebe Lal Shateri̇ %T New generalizations of Modular spaces %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 3 %R doi: 10.15672/hujms.531654 %U 10.15672/hujms.531654
ISNAD Lal Shateri̇, Tayebe . "New generalizations of Modular spaces". Hacettepe Journal of Mathematics and Statistics 49 / 3 (June 2020): 1076-1083 . https://doi.org/10.15672/hujms.531654
AMA Lal Shateri̇ T . New generalizations of Modular spaces. Hacettepe Journal of Mathematics and Statistics. 2020; 49(3): 1076-1083.
Vancouver Lal Shateri̇ T . New generalizations of Modular spaces. Hacettepe Journal of Mathematics and Statistics. 2020; 49(3): 1076-1083.