Henstock-Kurzweil type integral based on generalized g-semiring
We shall consider special class of generalized semiring based on generalized pseudo-operations of the following form: x circle plus y = g((-1)) (epsilong(x) + g(y)), x circle dot y = g((-1)) (g(x)(gamma) g(y)), where epsilon and gamma are arbitrary but fixed positive real numbers, g is a positive strictly monotone generating function and g((-1)) is its pseudo-inverse. Using this pseudo-operations, corresponding pseudo-measure and the Henstock-Kurzweil type integral will be introduced and investigated.
semiring generalized pseudo-operations pseudo-measure pseudo henstock-kurzweil integral