  The objective of this study is a better understanding of the relationships
between reduction and continuity. Solovay reduction is a variation of Turing
reduction based on the distance of two real numbers. We characterize Solovay
reduction by the existence of a certain real function that is computable (in
the sense of computable analysis) and Lipschitz continuous. We ask whether
there exists a reducibility concept that corresponds to H\"older continuity.
The answer is affirmative. We introduce quasi Solovay reduction and
characterize this new reduction via H\"older continuity. In addition, we
separate it from Solovay reduction and Turing reduction and investigate the
relationships between complete sets and partial randomness.
