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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 55 | Number 7 | Year 2018 | Article Id. IJMTT-V55P567 | DOI : https://doi.org/10.14445/22315373/IJMTT-V55P567

Hyperbolic Valued Signed Measure


Chinmay Ghosh, Sanjoy Biswas, Taha Yasin
Abstract

In this article we introduced two symbols D +¥ and D -¥ as extended hyperbolic numbers and modified the definition of hyperbolic valued measure. Also we defined hyperbolic valued signed measure and proved some theorems on it.

Keywords
Hyperbolic numbers, hyperbolic conjugation, idempotent representation, hyperbolic modulus, Dbounded, D-Cauchy sequence, D-valued measure, D-measure space, D-valued signed measure.
References

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[3] F. Catoni, D. Boccaletti, R. Cannata, V. Catoni, P. Zampetti: Geometry of Minkowski Space--Time, Springer (2011).
[4] R. Kumar, K. Sharma: Hyperbolic valued measures and Fundamental law of probability, Global Journal of Pure and Applied Mathematics, Vol. 13, No. 10 (2017), pp. 7163-7177.
[5] M. E. Luna-Elizarraras, M. Shapiro, D. C. Struppa, A. Vajiac: Bicomplex numbers and their elementary functions, Cubo A Mathematical Journal v. 14, No. 2 (2012), 61--80.
[6] M.E. Luna-Elizarraras, M. Shapiro, D. C. Struppa, A. Vajiac: Bicomplex holomorphic functions: The algebra, geometry and analysis of bicomplex numbers, Frontiers in Mathematics, Birkhäuser Basel, 2015.
[7] G. B. Price: An Introduction to Multicomplex Spaces and Functions, 3rd Edition, Marcel Dekker, New York, 1991.
[8] I. K. Rana: An Introduction to Measure and Integration, 2nd Edition, Narosa Publishing House, 2013.
[9] D. Rochan and M. Shapiro: On algebraic properties of bicomplex and hyperbolic numbers, Anal. Univ. Oradea, Fasc. Math. 11(2004), 71-- 110.

Citation :

Chinmay Ghosh, Sanjoy Biswas, Taha Yasin, "Hyperbolic Valued Signed Measure," International Journal of Mathematics Trends and Technology (IJMTT), vol. 55, no. 7, pp. 515-522, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V55P567

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