Functional equation and its modular stability with and without Δp-condition

Abstract

Mixed type is a further step of development in functional equations. In this paper, the authors made an attempt to introduce such equation of the following form with its general solution h(py + z) + h(py-z) + h(y + pz) + h(y-pz) = (p + p2)[h(y + z) + h(y-z)] + 2h(py)- 2(p2 + p-1)h(y) for all y,z ? R, p ? 0,?1. Also, without Fatou property authors investigate its various stabilities related to Ulam problem in modular space by considering with and without ?p-condition.