On bicomplex 𝔹ℂ-modules lp 𝕜(𝔹ℂ) and some of their geometric properties
-
Nilay Değirmen
and
Birsen Sağır
Abstract
In this paper, we examine the validity of bicomplex versions of some crucial
inequalities with respect to the hyperbolic-valued norm
References
[1] R. P. Agarwal, D. O’Regan and D. R. Sahu, Fixed Point Theory for Lipschitzian-type Mappings with Applications, Topol. Fixed Point Theory Appl. 6, Springer, New York, 2009. 10.1007/978-0-387-75818-3Search in Google Scholar
[2] D. Alpay, M. E. Luna-Elizarrarás, M. Shapiro and D. C. Struppa, Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis, Springer Briefs Math., Springer, Cham, 2014. 10.1007/978-3-319-05110-9Search in Google Scholar
[3] R. E. Castillo and H. Rafeiro, An Introductory Course in Lebesgue Spaces, CMS Books Math./Ouvrages Math. SMC, Springer, Cham, 2016. 10.1007/978-3-319-30034-4Search in Google Scholar
[4] M. Ciesielski and G. Lewicki, Sequence Lorentz spaces and their geometric structure, J. Geom. Anal. 29 (2019), no. 3, 1929–1952. 10.1007/s12220-018-0069-4Search in Google Scholar
[5]
N. Güngör,
Some geometric properties of the non-Newtonian sequence spaces
[6] R. Kumar and H. Saini, Topological bicomplex modules, Adv. Appl. Clifford Algebr. 26 (2016), no. 4, 1249–1270. 10.1007/s00006-016-0646-1Search in Google Scholar
[7]
R. Kumar, K. Singh, H. Saini and S. Kumar,
Bicomplex weighted Hardy spaces and bicomplex
[8] M. E. Luna-Elizarrarás, M. Shapiro, D. C. Struppa and A. Vajiac, Bicomplex Holomorphic Functions, Front. Math., Birkhäuser/Springer, Cham, 2015. 10.1007/978-3-319-24868-4Search in Google Scholar
[9] I. J. Maddox, Elements of Functional Analysis, 2nd ed., Cambridge University, Cambridge, 1988. Search in Google Scholar
[10]
O. Oğur,
Some geometric properties of weighted Lebesgue spaces
[11] G. B. Price, An Introduction to Multicomplex Spaces and Functions, Monogr. Textb. Pure Appl. Math. 140, Marcel Dekker, New York, 1991. Search in Google Scholar
[12] N. Sager and B. Sağır, On completeness of some bicomplex sequence spaces, Palest. J. Math. 9 (2020), no. 2, 1–12, 891–902. Search in Google Scholar
[13] N. Sager and B. Sağır, Some inequalities in quasi-Banach algebra of non-Newtonian bicomplex numbers, Filomat 35 (2021), no. 7, 2231–2243. 10.2298/FIL2107231SSearch in Google Scholar
[14] B. Sağır and İ. Alaşalvar, On geometric properties of weighted Lebesgue sequence spaces, Ikonion J. Math. 1 (2019), no. 1, 18–25. Search in Google Scholar
[15] C. Segre, Le rappresentazioni reali delle forme complesse e gli enti iperalgebrici, Math. Ann. 40 (1892), no. 3, 413–467. 10.1007/BF01443559Search in Google Scholar
[16] S. Singh and S. Dutta, On certain generalized mth order geometric difference sequence spaces, Far East J. Math. Sci. (FJMS) 116 (2019), no. 1, 83–100. 10.17654/MS116010083Search in Google Scholar
[17] S. Singh, S. Dutta, S. Dash and R. P. Sharma, Strongly summable Fibonacci difference geometric sequences defined by Orlicz functions, Ganita 71 (2021), no. 2, 99–109. Search in Google Scholar
[18] J. Yeh, Real Aalysis, 2nd ed., World Scientific, Hackensack, 2006. 10.1142/6023Search in Google Scholar
© 2022 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- On the well-posedness of nonlocal boundary value problems for a class of systems of linear generalized differential equations with singularities
- Products of Toeplitz operators with angular symbols
- Characterization of Lie-type higher derivations of triangular rings
- On classifying map of the integral Krichever–Hoehn formal group law
- Demicompactness perturbation in Banach algebras and some stability results
- On bicomplex 𝔹ℂ-modules lp 𝕜(𝔹ℂ) and some of their geometric properties
- On a class of nonlinear degenerate elliptic equations in weighted Sobolev spaces
- Asymptotic behaviors of solutions of a class of time-varying differential equations
- Fekete–Szegő problem of strongly α-close-to-convex functions associated with generalized fractional operator
- Some properties of Vitali sets
- Optimal conditions of solvability of periodic problem for systems of differential equations with argument deviation
- Generalized derivations with Engel condition on Lie ideals of prime rings
- Attractivity of implicit differential equations with composite fractional derivative
- Exponentially fitted difference scheme for singularly perturbed mixed integro-differential equations
Articles in the same Issue
- Frontmatter
- On the well-posedness of nonlocal boundary value problems for a class of systems of linear generalized differential equations with singularities
- Products of Toeplitz operators with angular symbols
- Characterization of Lie-type higher derivations of triangular rings
- On classifying map of the integral Krichever–Hoehn formal group law
- Demicompactness perturbation in Banach algebras and some stability results
- On bicomplex 𝔹ℂ-modules lp 𝕜(𝔹ℂ) and some of their geometric properties
- On a class of nonlinear degenerate elliptic equations in weighted Sobolev spaces
- Asymptotic behaviors of solutions of a class of time-varying differential equations
- Fekete–Szegő problem of strongly α-close-to-convex functions associated with generalized fractional operator
- Some properties of Vitali sets
- Optimal conditions of solvability of periodic problem for systems of differential equations with argument deviation
- Generalized derivations with Engel condition on Lie ideals of prime rings
- Attractivity of implicit differential equations with composite fractional derivative
- Exponentially fitted difference scheme for singularly perturbed mixed integro-differential equations
