Abstract

The current study defines and examines the concept of arithmetic continuity in quasi-cone metric spaces. This work introduces several new concepts, including forward and backward arithmetic convergence, arithmetic $ff$-continuity, $fb$-continuity, forward and backward arithmetic compactness, and uniform continuity. We have determined the conditions under which the uniform limit of an arithmetic $ff$-continuous function is again an arithmetic $ff$-continuous function. In quasi cone metric spaces, certain arithmetic compactness results are also proved. We have also proved some interesting results pertaining to these concepts.

Keywords and Phrases

Arithmetic continuity, arithmetic convergence, arithmetic compactness.

A.M.S. subject classification

40A35 40A05, 26A15.

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