In this paper we present a unified theory of convergence results in the study of abstract problems.
To this end we introduce a new mathematical object, the so-called Tykhonov triple , constructed by using a set of parameters , a multivalued function and a set of sequences . Given a problem and a Tykhonov triple , we introduce the notion of well-posedness of problem with respect to and provide several preliminary results, in the framework of metric spaces.
Then we show how these abstract results can be used to obtain various convergences
in the study of a nonlinear equation in reflexive Banach spaces.