Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

On Topological Bihyperbolic Modules


Affiliations
1 28, Dolua Dakshinpara Haridas Primary School Beldanga, Murshidabad Pin-742133, West Bengal, India
2 Department of Mathematics, Kazi Nazrul University, Nazrul Road, P.O.- Kalla C.H. Asansol-713340, West Bengal, India
3 Department of Mathematics University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal
     

   Subscribe/Renew Journal


In this paper, we introduce topological modules over the ring of bihyperbolic numbers. We discuss bihyperbolic convexity, bihyperbolic-valued seminorms and bihyperbolic-valued Minkowski functionals in topological bihyperbolic modules. Finally we introduce locally bihyperbolic convex modules.

Keywords

Bihyperbolic Modules, Topological Bihyperbolic Modules, Bihyperbolic Convexity, Bihyperbolic-Valued Seminorms, Bihyperbolic-Valued Minkowski Functionals, Locally Bihyperbolic Convex Modules.
Subscription Login to verify subscription
User
Notifications
Font Size


  • M. Bilgin and S. Ersoy, Algebraic properties of bihyperbolic numbers, Advances in Applied Clifford Algebras, 30 (1):13(2020).
  • J. Cockle, On certain functions resembling quaternions and on a new imaginary in algebra, Lond-Dublin-Edinb. Philos. Mag., 3 (33)(1848), 435-439.
  • R. Kumar, R. Kumar and D. Rochon, The fundamental theorems in the framework of bicomplex topological modules, arXiv: 1109.3424v1(2011).
  • R. Kumar and H. Saini, Topological bicomplex modules, Adv. Appl. Clifford Algebras, 26 (4)(2016), 1249-1270.
  • R. Larsen, Functional Analysis: An Introduction, Marcel Dekker, New York 1973.
  • M. E. Luna-Elizarraras, C. O. Perez-Regalado and M. Shapiro, On linear functionals and Hahn–Banach theorems for hyperbolic and bicomplex modules, Adv. Appl. Clifford Algebras, 24 (2014), 1105-1129.
  • L. Narici and E. Beckenstein, Topological Vector Spaces, Marcel Dekker, New York 1985.
  • S. Olariu, Complex Numbers in n-dimensions, North-Holland Mathematics Studies, Elsevier, Amsterdam, Boston, 190 (2002), 51-148.
  • A. A. Pogorui, R. M. Rodriguez-Dagnino and R. D. Rodrigue-Said, On the set of zeros of bihyperbolic polynomials, Complex Var. Elliptic Equ. 53 (7)(2008), 685-690.
  • W. Rudin, Functional Analysis, 2nd edn., McGraw Hill, New York 1991.
  • C. Segre, Le rappresentazioni reali delle forme complesse e gli enti iperalgebrici (The real representation of complex elements and hyperalgebraic entities), Math. Ann., 40 (1892), 413-467.

Abstract Views: 275

PDF Views: 3




  • On Topological Bihyperbolic Modules

Abstract Views: 275  |  PDF Views: 3

Authors

Soumen Mondal
28, Dolua Dakshinpara Haridas Primary School Beldanga, Murshidabad Pin-742133, West Bengal, India
Chinmay Ghosh
Department of Mathematics, Kazi Nazrul University, Nazrul Road, P.O.- Kalla C.H. Asansol-713340, West Bengal, India
Sanjib Kumar Datta
Department of Mathematics University of Kalyani, P.O.-Kalyani, Dist-Nadia, PIN-741235, West Bengal

Abstract


In this paper, we introduce topological modules over the ring of bihyperbolic numbers. We discuss bihyperbolic convexity, bihyperbolic-valued seminorms and bihyperbolic-valued Minkowski functionals in topological bihyperbolic modules. Finally we introduce locally bihyperbolic convex modules.

Keywords


Bihyperbolic Modules, Topological Bihyperbolic Modules, Bihyperbolic Convexity, Bihyperbolic-Valued Seminorms, Bihyperbolic-Valued Minkowski Functionals, Locally Bihyperbolic Convex Modules.

References





DOI: https://doi.org/10.18311/jims%2F2023%2F34192