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Bazı Newtonyen Olmayan Superposition Operatörlerin *-Sürekliliği ve *-Düzgün Sürekliliği Üzerine

Year 2021, Issue: 28, 959 - 967, 30.11.2021
https://doi.org/10.31590/ejosat.1012337

Abstract

Geçmişten günümüze superposition operatörler ve Newtonyen olmayan analiz üzerine birçok çalışma yapılmıştır. Sağır ve Erdoğan Newtonyen olmayan superposition operatörleri tanımlamış ve bazı dizi uzayları üzerinde karakterize etmişlerdir. Ayrıca c0,α ve cα uzaylarından l1,β uzayına tanımlı Newtonyen olmayan superposition operatörlerin *- sınırlılığını ve *-yerel sınırlılığını incelemişlerdir. Bu çalışmada operatörün *-süreklilik ve *-düzgün sürekliliğini tanımlıyoruz. c0,α uzayından l1,β uzayına tanımlı Newtonyen olmayan superposition operatörün *-sürekliliği için gerekli ve yeterli koşulları ispatlıyoruz. Sonra Newtonyen olmayan superposition operatörün *-düzgün sürekliliği ile *-sınırlılığı arasındaki ilişkiyi inceliyoruz. Ayrıca cα uzayından l1,β uzayına tanımlı Newtonyen olmayan superposition operatör için de benzer sonuçlar araştırılmıştır.

References

  • 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).
  • Thuangoon, A. “Continuity of superposition operators on some sequence spaces of Maddox”, Master of Sciences Dissertation, Graduate School of Chiang Mai University, 66, Thailand, (1998).
  • A. F. Çakmak and F. Başar, “Some new results on sequence spaces with respect to non-Newtonian calculus”, Journal of Inequalities and Applications, vol. 228, no.1, 1-17, (2012).
  • Sağır, B. ve Güngör, N. Continuity of Superposition Operators on the Double Sequence Spaces , Filomat, 9 , 2017-2118. (2015).
  • B. Sağır and N. Güngör, “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).
  • B. Sağır and F. Erdoğan, “On Characterization of Non- Newtonian Superposition Operators in Some Sequence Spaces”, Filomat, 33:9, 2601-2612, (2019).
  • [9] B. Sağır and F. Erdoğan, “On Function Sequences and Series in the Non-Newtonian Calculus”, Journal of Science and Arts, 4(49), 915-936, (2019).
  • F. Erdoğan and B. Sağır, “On *- Boundedness and *-Local Boundedness of Non-Newtonian Superposition Operators in and to ”, Journal of Universal Mathematics, 4(2), 241-251, (2021).
  • N.Sager and B. Sağır, .Some inequalities in quasi-Banach algebra of non-Newtonian bicomplex numbers., Filomat, 35(7), (2021).
  • Güngör, N. ve Sağır, B. Continuity of Superposition Operators on Double Sequence Spaces of Maddox , Iranian Journal of Science and Technology Transactions A: Science, doi:10.1007/s40995-017-0266-1, (2017).
  • C. Duyar, B. Sağır, O. Oğur, Some basic topological properties on non- Newtonian real line, British Journal of Mathematics and Computer Science, 9:4, 300-307, (2015).

On *-Continuity and *-Uniform Continuity of Some Non-Newtonian Superposition Operators

Year 2021, Issue: 28, 959 - 967, 30.11.2021
https://doi.org/10.31590/ejosat.1012337

Abstract

Many studies have been done on superposition operators and non-Newtonian calculus from past to present. Sağır and Erdoğan defined Non-Newtonian superposition operators and characterized them on some sequence spaces. Also they examined *- boundedness and *-locally boundedness of Non-Newtonian superposition operators c0,α and cα to l1,β. In this study, we define *-continuity and *-uniform continuity of operator. We have proved that the necessary and sufficient conditions for the *-continuity of the non-Newtonian superposition operator c0,α to l1,β. Then we examined the relationship between the *-uniform continuity and the *-boundedness of the non-Newtonian superposition operator. Also, the similar results have been researched for the Non-Newtonian superposition operator cα to l1,β.

References

  • 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).
  • Thuangoon, A. “Continuity of superposition operators on some sequence spaces of Maddox”, Master of Sciences Dissertation, Graduate School of Chiang Mai University, 66, Thailand, (1998).
  • A. F. Çakmak and F. Başar, “Some new results on sequence spaces with respect to non-Newtonian calculus”, Journal of Inequalities and Applications, vol. 228, no.1, 1-17, (2012).
  • Sağır, B. ve Güngör, N. Continuity of Superposition Operators on the Double Sequence Spaces , Filomat, 9 , 2017-2118. (2015).
  • B. Sağır and N. Güngör, “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).
  • B. Sağır and F. Erdoğan, “On Characterization of Non- Newtonian Superposition Operators in Some Sequence Spaces”, Filomat, 33:9, 2601-2612, (2019).
  • [9] B. Sağır and F. Erdoğan, “On Function Sequences and Series in the Non-Newtonian Calculus”, Journal of Science and Arts, 4(49), 915-936, (2019).
  • F. Erdoğan and B. Sağır, “On *- Boundedness and *-Local Boundedness of Non-Newtonian Superposition Operators in and to ”, Journal of Universal Mathematics, 4(2), 241-251, (2021).
  • N.Sager and B. Sağır, .Some inequalities in quasi-Banach algebra of non-Newtonian bicomplex numbers., Filomat, 35(7), (2021).
  • Güngör, N. ve Sağır, B. Continuity of Superposition Operators on Double Sequence Spaces of Maddox , Iranian Journal of Science and Technology Transactions A: Science, doi:10.1007/s40995-017-0266-1, (2017).
  • C. Duyar, B. Sağır, O. Oğur, Some basic topological properties on non- Newtonian real line, British Journal of Mathematics and Computer Science, 9:4, 300-307, (2015).
There are 13 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Fatmanur Erdogan 0000-0001-5638-5294

Birsen Sağır Duyar 0000-0001-5954-2005

Publication Date November 30, 2021
Published in Issue Year 2021 Issue: 28

Cite

APA Erdogan, F., & Sağır Duyar, B. (2021). On *-Continuity and *-Uniform Continuity of Some Non-Newtonian Superposition Operators. Avrupa Bilim Ve Teknoloji Dergisi(28), 959-967. https://doi.org/10.31590/ejosat.1012337