MODIFICATION OF REGULAR FUNCTIONS ON TERNARY REAL NUMBERS IN THE VIEW OF QUATERNION

Abstract

In this paper, we represent regular functions on ternary theory in the view of quaternion. By expressing quaternions using ternary number theory, a new form of regular function, called E-regular, is defined. From the defined regular function, we investigatethe properties of the appropriate hyper-conjugate harmonic functions and corresponding Cauchy-Riemann equations by pseudo-complex forms.