Anime-influenced animation or amerime is a type of media that refers to non-Japanese works of animation that emulate certain aspects of the visual style of Japanese anime. With the rise of anime's popularity it has become an integral part of animation produced in the Western world.
Generally, the term anime refers to a style of animation originating from Japan. As Japanese anime became increasingly popular, Western animation studios began implementing some visual stylizations typical in anime—such as exaggerated facial expressions and "super deformed" versions of characters. In particular, Batman Beyond displayed some characteristics of anime. Particularly for Batman Beyond, some of its production processes were outsourced to Japan.
The influence of Japanese anime on Western animation can be seen as far back as the 1980s, when animations such as Transformers were inspired by mecha anime (although the original Transformers anime was Japanese-animated, and its accompanying toy-line were re-issues of Japanese toys, so this may not count as an example). The influence of mecha anime on the Transformers franchise continues today, with the creators of Transformers Animated citing relatively recent Gainax productions, specifically Diebuster and Gurren Lagann, as major influences.
The advent of Japanese anime stylizations appearing in Western animation questioned the established meaning of "anime;" there are several Western animators who collaborated with Japanese anime creators while producing Western animation. For example, production on The Animatrix began when the Wachowskis visited some of the creators of the anime films that had been strong influences on their work, and decided to collaborate with them. The collaboration between Western and Japanese animators dates back to the mid-1960s, when it was produced The King Kong Show and Johnny Cypher in Dimension Zero.