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Some Geometric Properties of Bicomplex Sequence Spaces $l_{p}\left(\mathbb{BC}\right) $

Yıl 2022, Cilt: 10 Sayı: 1, 44 - 49, 15.04.2022

Öz

In this article, we examine some geometric properties such as convexity, strictly convexity, uniformly convexity of bicomplex sequence spaces $ l_{p}\left( \mathbb{BC}\right) $ with Euclidean norm by proving some significant inequalities. We also furnish some nontrivial examples that support our findings for geometric properties not provided in some of these bicomplex sequence spaces.

Kaynakça

  • [1] C. Segre, Le rappresentazioni reali delle forme complesse e gli enti iperalgebrici, Math. Ann., Vol:40, No.3 (1892), 413-467.
  • [2] G. B. Price, An introduction to multicomplex spaces and functions, M. Dekker, 1991.
  • [3] M. E. Luna-Elizarraras, M. Shapiro, D. C. Struppa and A. Vajiac, Bicomplex numbers and their elementary functions, Cubo (Temuco), Vol:14, No.2 (2012), 61-80.
  • [4] D. Alpay, M. E. Luna-Elizarrar´as, M. Shapiro and D. C. Struppa, Basics of functional analysis with bicomplex scalars, and bicomplex Schur analysis, Springer Science & Business Media, 2014.
  • [5] M. E. Luna-Elizarrar´as, M. Shapiro, D. C. Struppa and A. Vajiac, Bicomplex holomorphic functions: The algebra, geometry and analysis of bicomplex numbers, Birkh¨auser, 2015.
  • [6] N. Sager and B. Sa˘gır, On completeness of some bicomplex sequence spaces, Palest. J. Math., Vol:9, No.2 (2020), 891-902.
  • [7] R. P. Agarwal, D. O’Regan and D. R. Sahu, Fixed point theory for Lipschitzian-type mappings with applications (Vol. 6), New York:Springer, 2006.
  • [8] R. E. Castillo and H. Rafeiro, An introductory course in Lebesgue spaces, Switzerland: Springer, 2016.
  • [9] B. Sa˘gır and˙I Alas¸alvar, On geometric properties of weighted Lebesgue sequence spaces, Ikonion Journal of Mathematics, Vol:1, No.1 (2019), 18-25.
  • [10] N. G¨ung¨or, Some geometric properties of the non-Newtonian sequence spaces lp (N), Math. Slovaca, Vol:70, No.3 (2020), 689-696.
  • [11] G. K¨othe, Topological vector spaces I, Springer-Verlag Berlin, Heidelberg, 1983.
  • [12] H. Jarchow, Locally convex space, BG Teubner, Stuttgart, 1981.
  • [13] J. Yeh, Real Analysis: Theory of measure and integration second edition, World Scientific Publishing Company, 2006.
Yıl 2022, Cilt: 10 Sayı: 1, 44 - 49, 15.04.2022

Öz

Kaynakça

  • [1] C. Segre, Le rappresentazioni reali delle forme complesse e gli enti iperalgebrici, Math. Ann., Vol:40, No.3 (1892), 413-467.
  • [2] G. B. Price, An introduction to multicomplex spaces and functions, M. Dekker, 1991.
  • [3] M. E. Luna-Elizarraras, M. Shapiro, D. C. Struppa and A. Vajiac, Bicomplex numbers and their elementary functions, Cubo (Temuco), Vol:14, No.2 (2012), 61-80.
  • [4] D. Alpay, M. E. Luna-Elizarrar´as, M. Shapiro and D. C. Struppa, Basics of functional analysis with bicomplex scalars, and bicomplex Schur analysis, Springer Science & Business Media, 2014.
  • [5] M. E. Luna-Elizarrar´as, M. Shapiro, D. C. Struppa and A. Vajiac, Bicomplex holomorphic functions: The algebra, geometry and analysis of bicomplex numbers, Birkh¨auser, 2015.
  • [6] N. Sager and B. Sa˘gır, On completeness of some bicomplex sequence spaces, Palest. J. Math., Vol:9, No.2 (2020), 891-902.
  • [7] R. P. Agarwal, D. O’Regan and D. R. Sahu, Fixed point theory for Lipschitzian-type mappings with applications (Vol. 6), New York:Springer, 2006.
  • [8] R. E. Castillo and H. Rafeiro, An introductory course in Lebesgue spaces, Switzerland: Springer, 2016.
  • [9] B. Sa˘gır and˙I Alas¸alvar, On geometric properties of weighted Lebesgue sequence spaces, Ikonion Journal of Mathematics, Vol:1, No.1 (2019), 18-25.
  • [10] N. G¨ung¨or, Some geometric properties of the non-Newtonian sequence spaces lp (N), Math. Slovaca, Vol:70, No.3 (2020), 689-696.
  • [11] G. K¨othe, Topological vector spaces I, Springer-Verlag Berlin, Heidelberg, 1983.
  • [12] H. Jarchow, Locally convex space, BG Teubner, Stuttgart, 1981.
  • [13] J. Yeh, Real Analysis: Theory of measure and integration second edition, World Scientific Publishing Company, 2006.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Nilay Değirmen 0000-0001-8192-8473

Birsen Sağır Duyar 0000-0001-5954-2005

Yayımlanma Tarihi 15 Nisan 2022
Gönderilme Tarihi 13 Ağustos 2021
Kabul Tarihi 22 Mart 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 10 Sayı: 1

Kaynak Göster

APA Değirmen, N., & Sağır Duyar, B. (2022). Some Geometric Properties of Bicomplex Sequence Spaces $l_{p}\left(\mathbb{BC}\right) $. Konuralp Journal of Mathematics, 10(1), 44-49.
AMA Değirmen N, Sağır Duyar B. Some Geometric Properties of Bicomplex Sequence Spaces $l_{p}\left(\mathbb{BC}\right) $. Konuralp J. Math. Nisan 2022;10(1):44-49.
Chicago Değirmen, Nilay, ve Birsen Sağır Duyar. “Some Geometric Properties of Bicomplex Sequence Spaces $l_{p}\left(\mathbb{BC}\right) $”. Konuralp Journal of Mathematics 10, sy. 1 (Nisan 2022): 44-49.
EndNote Değirmen N, Sağır Duyar B (01 Nisan 2022) Some Geometric Properties of Bicomplex Sequence Spaces $l_{p}\left(\mathbb{BC}\right) $. Konuralp Journal of Mathematics 10 1 44–49.
IEEE N. Değirmen ve B. Sağır Duyar, “Some Geometric Properties of Bicomplex Sequence Spaces $l_{p}\left(\mathbb{BC}\right) $”, Konuralp J. Math., c. 10, sy. 1, ss. 44–49, 2022.
ISNAD Değirmen, Nilay - Sağır Duyar, Birsen. “Some Geometric Properties of Bicomplex Sequence Spaces $l_{p}\left(\mathbb{BC}\right) $”. Konuralp Journal of Mathematics 10/1 (Nisan 2022), 44-49.
JAMA Değirmen N, Sağır Duyar B. Some Geometric Properties of Bicomplex Sequence Spaces $l_{p}\left(\mathbb{BC}\right) $. Konuralp J. Math. 2022;10:44–49.
MLA Değirmen, Nilay ve Birsen Sağır Duyar. “Some Geometric Properties of Bicomplex Sequence Spaces $l_{p}\left(\mathbb{BC}\right) $”. Konuralp Journal of Mathematics, c. 10, sy. 1, 2022, ss. 44-49.
Vancouver Değirmen N, Sağır Duyar B. Some Geometric Properties of Bicomplex Sequence Spaces $l_{p}\left(\mathbb{BC}\right) $. Konuralp J. Math. 2022;10(1):44-9.
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