Analytical Expression Of Some Parameters Family Of Functional Functions And Their Holder Exponents

Continuity and differentiability are important concepts in classical analysis. Since Weierstrass function was constructed, which is the first continuous but nowhere differentiable function, more and more mathematicians are focusing on constructing this kind of new functions and study their properties. The paper gives analytical expressions of generalized Okamoto function Fa,b,r(x) using generalized ternary num-ber system B containing parameter r, and then their fractal properties are studied. Based on a classification of ternary self-similar set, we consider analytical expres-sions of a parameter family of functional equations and study their fractal properties including Holder exponents.