Some basic results on the sets of sequences with geometric calculus

As 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 …eld C(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 de…ne the sets !(G), `1(G), c(G), c 0 (G) and `p(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 vector space on the …eld C(G) and a complete metric space.