Marcel Mauss (1872-1950) French sociologist and anthropologist, nephew of Durkheim, pioneered functionalist analysis in anthropology in his study of the role of ostentatious shows of gift-making in Native Americans (function was explained as disposing of a potentially disruptive surplus produce). A similarly less judgmental and more objective, albeit atheoretical, approach was already being taken up by Boas and others of his school.
Bronislaw Malinowski (1884-1942) Born in Poland, emigrated to UK and then to USA; (working at the same time as Sapir) founded Functionalism in Social Anthropology: all components of society interlock to form a well-balanced system; integrated view of characteristics like beliefs, ceremonies, customs, institutions, religion, ritual and sexual taboos. Like Bloomfield and Boas he emphasised detailed collection of data.
``The functional view of culture lays down the principle that in every type of civilization, every custom, material object, idea and belief fulfills some vital function, has some task to accomplish, represents an indispensable part with a working whole.''
Quote taken from
http://emuseum.mnsu.edu/information/biography/klmno/malinowski_bronislaw (which cites Kardiner and Preble, 1961, but contains many typos).
In 1915-18 Malimowski studied the Trobriand Islanders of New Guinea in the southwest Pacific Argonauts of the Western Pacific (1922); used a holistic approach in studying social interactions, finding associations with magic, religion, kinship and trade; contributed to a cross-cultural study of psychology through observations of the relationships of kinship; discovered evidence to discredit Freud's theory of the Oedipus Complex in the lives of the Trobianders. Later he did field work in Africa and Mexico.
Books by Malinowski: The Trobriand Islands (1915); Argonauts of the Western Pacific (1922); The Scientific Theory of Culture (1922).
Posthumous Books: Magic, Science, and Religion (1948); The Dynamics of Culture Change (1961).
See also Radcliffe-Brown and E.E. Evans-Pritchard