The notion of left-right (resp. right-left) symmetric biderivation of KU-algebras is introduced and some related properties are investigated.

With the deep study in this work, we introduce the concept of filters of a bitonic algebra A. We study some fundamental structures of such determined filters. We also focus on features of filters with respect to homomorphisms. With the help of the idea of upper sets, we investigate basic ideas of filters in a bitonic algebra, and we also state some important theorems related to them. We obtain some relations between filters of bitonic algebras and upper sets. We obtain an equivalent condition of the filters with the help of the notion of upper sets.

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In this study, we introduce the notion of * and +-symmetric bi-multipliers in incline algebras and research some related properties. Also, we define kernel of * and +-symmetric bi-multipliers in incline algebras. Additionally, we state some properties of these * and +-symmetric bi-multipliers in integral incline algebras.