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Some basic results on the sets of sequences with geometric calculus
AIP Conf. Proc. 1470, pp. 95-98; doi:http://dx.doi.org/10.1063/1.4747648 (4 pages)
FIRST INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS: ICAAM 2012
Date:
18–21 October 2012
Location:
Gumushane, Turkey
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Add to FacebookAs an alternative to the classical calculus, Grossman and Katz [Non-Newtonian Calculus, Lee Press, Pigeon Cove, Massachusetts, 1972] introduced the non-Newtonian calculus consisting of the branches of geometric, anageometric and bigeometric calculus. Following Grossman and Katz, we construct the field 
(G) of geometric complex numbers and the concept of geometric metric. Also we give the triangle and Minkowski's inequalities in the sense of geometric calculus. Later we respectively define the sets w(G), ℓ∞(G), c(G), c0(G) and ℓp(G) of all, bounded, convergent, null and p-absolutely summable sequences, in the sense of geometric calculus and show that each of the set forms a complete vector space on the field (G).
(G) of geometric complex numbers and the concept of geometric metric. Also we give the triangle and Minkowski's inequalities in the sense of geometric calculus. Later we respectively define the sets w(G), ℓ∞(G), c(G), c0(G) and ℓp(G) of all, bounded, convergent, null and p-absolutely summable sequences, in the sense of geometric calculus and show that each of the set forms a complete vector space on the field (G).© 2012 American Institute of Physics
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