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.
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Year 2022,
Volume: 10 Issue: 1, 44 - 49, 15.04.2022
Nilay Değirmen
,
Birsen Sağır Duyar
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.
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- [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.
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