Statistically convergent difference sequences of bi-complex numbers
-
Subhajit Bera
and
Binod Chandra Tripathy
Abstract
In this article we introduce the notion of statistical convergence difference sequences of bi-complex numbers. Some properties of these sequence spaces like BC-module, Banach BC-module, BC-balanced set, BC-convex set, solidness, and symetricity are studied.
References
[1] S. Bera and B. C. Tripathy, Statistical bounded sequences of bi-complex numbers, Probl. Anal. Issues Anal. 12(30) (2023), no. 2, 3–16. 10.15393/j3.art.2023.13090Search in Google Scholar
[2] S. Bera and B. C. Tripathy, Statistical convergence in a bicomplex valued metric space, Ural Math. J. 9 (2023), no. 1, 49–63. 10.15826/umj.2023.1.004Search in Google Scholar
[3] R. C. Buck, Generalized asymptotic density, Amer. J. Math. 75 (1953), 335–346. 10.2307/2372456Search in Google Scholar
[4] J. Cockle, A new imaginary in algebra, Lond. Edinb. Philos. Mag. 33 (1848), no. 3, 345–349. 10.1080/14786444808646139Search in Google Scholar
[5]
B. Das and B. C. Tripathy,
On
[6] B. Das, P. Debnath and B. C. Tripathy, On statistically convergent complex uncertain sequences, Carpathian Math. Publ. 14 (2022), no. 1, 135–146. 10.15330/cmp.14.1.135-146Search in Google Scholar
[7] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244. 10.4064/cm-2-3-4-241-244Search in Google Scholar
[8] J. A. Fridy, On statistical convergence, Analysis 5 (1985), no. 4, 301–313. 10.1524/anly.1985.5.4.301Search in Google Scholar
[9] J. A. Fridy and C. Orhan, Statistical limit superior and limit inferior, Proc. Amer. Math. Soc. 125 (1997), no. 12, 3625–3631. 10.1090/S0002-9939-97-04000-8Search in Google Scholar
[10] H. Kızmaz, On certain sequence spaces, Canad. Math. Bull. 24 (1981), no. 2, 169–176. 10.4153/CMB-1981-027-5Search in Google Scholar
[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] D. Rochon and M. Shapiro, On algebraic properties of bicomplex and hyperbolic numbers, An. Univ. Oradea Fasc. Mat. 11 (2004), 71–110. Search in Google Scholar
[13] T. Šalát, On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), no. 2, 139–150. Search in Google Scholar
[14] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361–375. 10.2307/2308747Search 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] B. C. Tripathy, On statistically convergent and statistically bounded sequences, Bull. Malaysian Math. Soc. (2) 20 (1997), no. 1, 31–33. Search in Google Scholar
[17] B. C. Tripathy and P. K. Nath, Statistical convergence of complex uncertain sequences, New Math. Nat. Comput. 13 (2017), no. 3, 359–374. 10.1142/S1793005717500090Search in Google Scholar
[18] B. C. Tripathy and M. Sen, On generalized statistically convergent sequences, Indian J. Pure Appl. Math. 32 (2001), no. 11, 1689–1694. Search in Google Scholar
[19] A. Zygmund, Trigonometric Series: Vol. II, Cambridge University, New York, 1993. Search in Google Scholar
© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- On the Laplace transform
- An uncertainty principle for the windowed Bochner–Fourier transform with the complex-valued window function
- Controllability result in α-norm for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces
- Polynomial convergence of iterations of certain random operators in Hilbert space
- Trigonometric approximation of signals (functions) belonging to certain Lipschitz spaces using C δ.C operator
- Almost compactness in neutrosophic topological spaces
- Some results for a weakly coupled system of semi-linear structurally damped σ-evolution equations
- On the stochastic elliptic equations involving fractional derivative
- A note on Köthe–Toeplitz duals and multiplier spaces of sequence spaces involving bicomplex numbers
- A brief survey on the development and applications of Goebel’s coincidence point theorem in differential and integral equations
- Boundary controllability for variable coefficients one-dimensional wave equation with interior degeneracy
- On random pairwise comparisons matrices and their geometry
- Statistically convergent difference sequences of bi-complex numbers
- On some inequalities concerning polynomials with restricted zeros
- New retarded nonlinear integral inequalities of Gronwall–Bellman–Pachpatte type and their applications
- On a new variant of cyclic (noncyclic) condensing operators with existence of optimal solutions to an FDE
- Exponential stability of non-conformable fractional-order systems
Articles in the same Issue
- Frontmatter
- On the Laplace transform
- An uncertainty principle for the windowed Bochner–Fourier transform with the complex-valued window function
- Controllability result in α-norm for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces
- Polynomial convergence of iterations of certain random operators in Hilbert space
- Trigonometric approximation of signals (functions) belonging to certain Lipschitz spaces using C δ.C operator
- Almost compactness in neutrosophic topological spaces
- Some results for a weakly coupled system of semi-linear structurally damped σ-evolution equations
- On the stochastic elliptic equations involving fractional derivative
- A note on Köthe–Toeplitz duals and multiplier spaces of sequence spaces involving bicomplex numbers
- A brief survey on the development and applications of Goebel’s coincidence point theorem in differential and integral equations
- Boundary controllability for variable coefficients one-dimensional wave equation with interior degeneracy
- On random pairwise comparisons matrices and their geometry
- Statistically convergent difference sequences of bi-complex numbers
- On some inequalities concerning polynomials with restricted zeros
- New retarded nonlinear integral inequalities of Gronwall–Bellman–Pachpatte type and their applications
- On a new variant of cyclic (noncyclic) condensing operators with existence of optimal solutions to an FDE
- Exponential stability of non-conformable fractional-order systems
