Euler Totient Matrisi Tarafından Tanımlanan Yeni Bir Paranormlu Dizi Uzayı

Yıl 2019, Cilt: 9 Sayı: 2, 277 - 282, 01.06.2019

Merve İlkhan Serkan Demiriz Emrah Evren Kara

https://doi.org/10.7212/zkufbd.v9i2.1469

Öz

Bu çalışmada, Euler Totient fonksiyonu ile oluşturulan regüler bir matrisin kullanılmasıyla, yeni bir paranormlu uzay olan , Φ,p uzayını tanımladık ve bu uzayın , p uzayına lineer izomorf olduğunu gösterdik. Ayrıca bu uzayın α-,β-,γ-duallerini ve Schauder bazını hesapladık

Anahtar Kelimeler

α-, β-, γ-dualleri, Euler totient fonksiyonu, Möbius fonksiyonu, Paranormlu dizi uzayı

A New Paranormed Sequence Space Defined by Euler Totient Matrix

Öz

In the present paper, by using the regular matrix given by Euler Totient function, we give a new paranormed sequence space l Φ,p and prove that the spaces l Φ,p and l p are linearly isomorphic. Also, we compute some dual spaces and the Schauder basis of this space.

Anahtar Kelimeler

Paranormed sequence space, α-, β-, γ-duals, Euler totient function, Möbius function.

Kaynakça

• Altay, B., Başar, F. 2002. On the paranormed Riesz sequence spaces of non-absolute type. Southeast Asian Bull. Math., 26(5):701-715.
• Altay, B., Başar, F. 2006. Some paranormed Riesz sequence spaces of non-absolute type. Southeast Asian Bull. Math., 30:591-608. Aydın, C., Başar, F. 2004. Some new paranormed sequence spaces, Inform. Sci., 160:27-40.
• Aydın, C., Başar, F. 2006. Some generalizations of the sequence space ar p . Iran. Sci. Technol. Trans. A. Sci., 30(A2):175-190.
• Başar, F. 2012. Summability theory and its applications, Bentham Science Publishers, e-books, Monographs, İstanbul.
• Candan, M. 2014. A new sequence space isomorphic to the space ,^ h p and compact operators. J. Math. Comput. Sci., 4(2):306- 334.
• Candan, M. 2014. Almost convergence and double sequential band matrix. Acta Math. Sci. Ser. B Engl. Ed., 34(2):354-366.
• Candan, M. 2015. A new perspective on paranormed Riesz sequence space of non-absolute type. Glob. J. Math. Anal., 3(4):150-163.
• Candan, M., Güneş, A. 2015. Paranormed sequence space of non-absolute type founded using generalized difference matrix. Proc. Natl. Acad. Sci. India Sect. A, 85(2):269-276.
• Candan, M., Kılınç, G. 2015. A different look for paranormed Riesz sequence space derived by Fibonacci matrix. Konuralp J. Math., 3(2):62-76.
• Demiriz, S., Çakan, C. 2010. On some new paranormed Euler sequence spaces and Euler core. Acta. Math. Sin. (Eng. Ser.), 26(7):1207-1222.
• Ellidokuzoğlu, H.B., Demiriz, S. 2016. On the paranormed Taylor sequence spaces. Konuralp J. Math., 4(2):132-148.
• Et, M., Başarır, M. 1997. On some generalized difference sequence spaces. Period. Math. Hung., 35(3):169-175.
• Et, M., Çolak, R. 1995. On some gerneralized difference sequence spaces. Soochow J. Math., 21(4):377-386.
• Grosse-Erdmann, KG. 1993. Matrix transformations between the sequence spaces of Maddox. J. Math. Anal. Appl., 180(1):223- 238.
• İlkhan, M., Kara, EE. 2019. A new Banach space defined by Euler totient matrix operator. Oper Matrices., 13(2):527-544.
• Kama, R., Altay, B. 2017. Weakly unconditionally Cauchy series and Fibonacci sequence spaces. J. Inequal. Appl., 2017, 133 doi: 10.1186/s13660-017-1407-y.
• Kama, R., Altay, B., Başar, F. 2018. On the domains of backward difference matrix and the spaces of convergence of a series. Bull. Allahabad Math. Soc., 33(1):139-153.
• Kara, EE., Öztürk, M., Başarır, M. 2010. Some topological and geometric properties of generalized Euler sequence space. Math. Slovaca, 60(3): 385-398.
• Karakaya, V., Şimşek, N. 2012. On some properties of new paranormed sequence space of nonabsolute type. Abstr. Appl. Anal., 2012: Article ID 921613, 10 pages . Kılınç, G., Candan, M. 2017 A different approach for almost sequence spaces defined by a generalized weighted mean. Sakarya Univ. J. Sci., 21(6):1529-1536.
• Kovac, E. 2005. On { - convergence and { - density. Math. Slovaca, 55:329-351.
• Maddox, I.J. 1967. Spaces of strongly summable sequences. Quart. J. Math. Oxford, 18(2): 344-355.
• Maddox, I.J. 1988. Elements of functional analysis, (2nd edition). The University Press, Cambridge.
• Nakano, H. 1951. Modulared sequence spaces. Proc. Jpn. Acad, 27(2):508-512.
• Niven, I., Zuckerman, H.S., Montgomery, H.L. 1991. An introduction to the theory of numbers, (5th edition). Wiley, New York.
• Schoenberg, I. 1959. The integrability of certain functions and related summability methods. Amer. Math. Monthly, 66:361- 375.
• Simons, S. 1965. The sequence spaces ,^ h pv and m p^ hv . Proc. London Math. Soc. 15(3): 422-436.