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

Year 2022, Volume: 10 Issue: 1, 44 - 49, 15.04.2022

Nilay Değirmen , Birsen Sağır Duyar

Abstract

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.

Keywords

bicomplex sequence spaces, convexity, strictly convexity, uniformly convexity

References

• [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.