Altering distances, some generalizations of Meir - Keeler theorems and applications

The purpose of this paper is to prove a general theorem of Meir - Keeler type using the notion of altering distance for occasionally weakly compatible mappings satisfying an implicit relation. As application, a problem of Meir - Keeler type satisfying a condition of integral type becomes a special case of a problem of Meir - Keeler type with an altering distance.