On various restricted sumsets

For finite subsets A1,…,An of a field, their sumset is given by {a1+⋯+an:a1∈A1,…,an∈An}. In this paper, we study various restricted sumsets of A1,…,An with restrictions of the following forms:ai-aj∉Sij,orαiai≠αjaj,orai+bi≢aj+bj(modmij).Furthermore, we gain an insight into relations among recent results on this area obtained in quite different ways.