Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, , 241 - 251, 31.07.2021
https://doi.org/10.33773/jum.954104

Öz

Kaynakça

  • M. Grossman and R. Katz, "Non-Newtonian Calculus", 1st ed., Lee Press, Pigeon Cove Massachussets, (1972).
  • F. Dedagich and P.P. Zabreiko, "Operator superpositions in the spaces lp ", Sibirskii Matematicheskii Zhurnal, 28, 86-98, (1987).
  • P. Tainchai, "Boundedness of superposition operators on some sequence spaces", Master of Sciences Dissertation, Graduate School of Chiang Mai University, 40, Thailand,(1996).
  • A. Sama-ae, "Boundedness of superposition operators on the sequence spaces of Maddox", Master of Sciences Dissertation, Graduate School of Chiang Mai University, 55, Thailand, (1997).
  • A. F. Cakmak and F. Basar, "Some new results on sequence spaces with respect to non-Newtonian calculus", Journal of Inequalities and Applications, vol. 228, no.1, 1-17, (2012).
  • B. Sagır and N. Gungor, "Locally Boundedness and Continuity of Superposition Operators on the Double Sequence Spaces Cr0", Journal of Computational Analysis and Applications, vol. 19(2), 365-377, (2015).
  • C. Duyar and M. Erdogan, "On non-Newtonian real number series", IOSR Journal of Mathematics, vol. 12, iss. 6, ver. IV, 34-48, (2016).
  • O. Ogur, "On characterization of boundedness of superposition operators on the Maddox space Cr0(p) of double sequences", New Trends in Mathematical Sciences, 4, 80-88, (2017).
  • B. Sagır and F. Erdogan, "On Characterization of Non-Newtonian Superposition Operators in Some Sequence Spaces", Filomat, 33:9, 2601-2612, (2019).
  • B. Sagır and F. Erdogan, "On Function Sequences and Series in the Non-Newtonian Calculus", Journal of Science and Arts, 4(49), 915-936, (2019).
  • N. Gungor, "Some geometric properties of the non-Newtonian sequence spaces lp(N)", Mathematica Slovaca, vol. 70:3, 689-696, (2020).

ON *-BOUNDEDNESS AND *-LOCAL BOUNDEDNESS OF NON-NEWTONIAN SUPERPOSITION OPERATORS IN c_(0,α) AND c_α TO l_(1,β)

Yıl 2021, , 241 - 251, 31.07.2021
https://doi.org/10.33773/jum.954104

Öz

Many investigations have been made about of Non-Newtonian calculus and superposition operators until today. Non-Newtonian superposition operator was defined by Sağır and Erdoğan in [9]. In this study, we have defined *- boundedness and *-locally boundedness of operator. We have proved that the non-Newtonian superposition operator $_{N}P_{f}:c_{_{0,\alpha }}\rightarrow \ell _{1,\beta }$ is *-locally bounded if and only if f satisfies the condition (NA₂′). Then we have shown that the necessary and sufficient conditions for the *-boundedness of $% _{N}P_{f}:c_{_{0,\alpha }}\rightarrow \ell _{1,\beta }$ . Finally, the similar results have been also obtained for $_{N}P_{f}:c_{\alpha }\rightarrow \ell _{1,\beta }$ .

Kaynakça

  • M. Grossman and R. Katz, "Non-Newtonian Calculus", 1st ed., Lee Press, Pigeon Cove Massachussets, (1972).
  • F. Dedagich and P.P. Zabreiko, "Operator superpositions in the spaces lp ", Sibirskii Matematicheskii Zhurnal, 28, 86-98, (1987).
  • P. Tainchai, "Boundedness of superposition operators on some sequence spaces", Master of Sciences Dissertation, Graduate School of Chiang Mai University, 40, Thailand,(1996).
  • A. Sama-ae, "Boundedness of superposition operators on the sequence spaces of Maddox", Master of Sciences Dissertation, Graduate School of Chiang Mai University, 55, Thailand, (1997).
  • A. F. Cakmak and F. Basar, "Some new results on sequence spaces with respect to non-Newtonian calculus", Journal of Inequalities and Applications, vol. 228, no.1, 1-17, (2012).
  • B. Sagır and N. Gungor, "Locally Boundedness and Continuity of Superposition Operators on the Double Sequence Spaces Cr0", Journal of Computational Analysis and Applications, vol. 19(2), 365-377, (2015).
  • C. Duyar and M. Erdogan, "On non-Newtonian real number series", IOSR Journal of Mathematics, vol. 12, iss. 6, ver. IV, 34-48, (2016).
  • O. Ogur, "On characterization of boundedness of superposition operators on the Maddox space Cr0(p) of double sequences", New Trends in Mathematical Sciences, 4, 80-88, (2017).
  • B. Sagır and F. Erdogan, "On Characterization of Non-Newtonian Superposition Operators in Some Sequence Spaces", Filomat, 33:9, 2601-2612, (2019).
  • B. Sagır and F. Erdogan, "On Function Sequences and Series in the Non-Newtonian Calculus", Journal of Science and Arts, 4(49), 915-936, (2019).
  • N. Gungor, "Some geometric properties of the non-Newtonian sequence spaces lp(N)", Mathematica Slovaca, vol. 70:3, 689-696, (2020).
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Fatmanur Erdogan 0000-0001-5638-5294

Birsen Sağır Duyar 0000-0001-5954-2005

Yayımlanma Tarihi 31 Temmuz 2021
Gönderilme Tarihi 13 Temmuz 2021
Kabul Tarihi 29 Temmuz 2021
Yayımlandığı Sayı Yıl 2021

Kaynak Göster

APA Erdogan, F., & Sağır Duyar, B. (2021). ON *-BOUNDEDNESS AND *-LOCAL BOUNDEDNESS OF NON-NEWTONIAN SUPERPOSITION OPERATORS IN c_(0,α) AND c_α TO l_(1,β). Journal of Universal Mathematics, 4(2), 241-251. https://doi.org/10.33773/jum.954104
AMA Erdogan F, Sağır Duyar B. ON *-BOUNDEDNESS AND *-LOCAL BOUNDEDNESS OF NON-NEWTONIAN SUPERPOSITION OPERATORS IN c_(0,α) AND c_α TO l_(1,β). JUM. Temmuz 2021;4(2):241-251. doi:10.33773/jum.954104
Chicago Erdogan, Fatmanur, ve Birsen Sağır Duyar. “ON *-BOUNDEDNESS AND *-LOCAL BOUNDEDNESS OF NON-NEWTONIAN SUPERPOSITION OPERATORS IN c_(0,α) AND c_α TO l_(1,β)”. Journal of Universal Mathematics 4, sy. 2 (Temmuz 2021): 241-51. https://doi.org/10.33773/jum.954104.
EndNote Erdogan F, Sağır Duyar B (01 Temmuz 2021) ON *-BOUNDEDNESS AND *-LOCAL BOUNDEDNESS OF NON-NEWTONIAN SUPERPOSITION OPERATORS IN c_(0,α) AND c_α TO l_(1,β). Journal of Universal Mathematics 4 2 241–251.
IEEE F. Erdogan ve B. Sağır Duyar, “ON *-BOUNDEDNESS AND *-LOCAL BOUNDEDNESS OF NON-NEWTONIAN SUPERPOSITION OPERATORS IN c_(0,α) AND c_α TO l_(1,β)”, JUM, c. 4, sy. 2, ss. 241–251, 2021, doi: 10.33773/jum.954104.
ISNAD Erdogan, Fatmanur - Sağır Duyar, Birsen. “ON *-BOUNDEDNESS AND *-LOCAL BOUNDEDNESS OF NON-NEWTONIAN SUPERPOSITION OPERATORS IN c_(0,α) AND c_α TO l_(1,β)”. Journal of Universal Mathematics 4/2 (Temmuz 2021), 241-251. https://doi.org/10.33773/jum.954104.
JAMA Erdogan F, Sağır Duyar B. ON *-BOUNDEDNESS AND *-LOCAL BOUNDEDNESS OF NON-NEWTONIAN SUPERPOSITION OPERATORS IN c_(0,α) AND c_α TO l_(1,β). JUM. 2021;4:241–251.
MLA Erdogan, Fatmanur ve Birsen Sağır Duyar. “ON *-BOUNDEDNESS AND *-LOCAL BOUNDEDNESS OF NON-NEWTONIAN SUPERPOSITION OPERATORS IN c_(0,α) AND c_α TO l_(1,β)”. Journal of Universal Mathematics, c. 4, sy. 2, 2021, ss. 241-5, doi:10.33773/jum.954104.
Vancouver Erdogan F, Sağır Duyar B. ON *-BOUNDEDNESS AND *-LOCAL BOUNDEDNESS OF NON-NEWTONIAN SUPERPOSITION OPERATORS IN c_(0,α) AND c_α TO l_(1,β). JUM. 2021;4(2):241-5.