GENERALIZED SEQUENTIAL FEYNMAN INTEGRAL and FOURIER–FEYNMAN TRANSFORM

We introduce the concepts of a generalized sequential Feynman integral and a generalized sequential Fourier–Feynman transform. Existence theorems of these integral and transform are obtained for functionals in a Banach algebra Ŝ and some related functionals. Also we give a simple proof of a translation theorem for generalized sequential Feynman integral. Previous results on sequential Feynman integral and sequential Fourier–Feynman transform can be obtained as corollaries of our results. In the last section we introduce the concept of translation invariant generalized sequential Feynman integral.