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Spaces of continuous and bounded functions over the field of geometric complex numbersCakir, ZaferAlgebraic structures with respect to non-Newtonian calculusNon-Newtonian calculusNon-Newtonian function spaceFollowing Grossman and Katz (Non-Newtonian Calculus, 1972), we construct the sets B(A) and C(A) of geometric complex-valued bounded and continuous functions, where A denotes the compact subset of the complex plane C. We show that the sets B(A) and C(A) of complex-valued bounded and continuous functions form a vector space with respect to the addition and scalar multiplication in the sense of multiplicative calculus. Finally, we prove that B(A) and C(A) are complete metric spaces.SPRINGEROPEN2013Articlehttps://rdlopen.rawdatalibrary.net/r/gumushane/12081https://doi.org/10.1186/1029-242x-2013-3631029-242XenJournal of Inequalities and Applicationsinfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://gumushane-rdlopen.rawdatalibrary.net/tr/items/gumushane/12081