A fixed point theorem and Ulam stability of a general linear functional equation in random normed spaces

Abstract We prove a very general fixed point theorem in the space of functions taking values random normed (RN-space). Next, we show several its consequences and, among others, present applications it proving Ulam stability results for inhomogeneous linear functional equation with variables class f mapping vector X into an RN-space. Particular cases are instance equations Cauchy, Jensen, Jordan–von Neumann, Drygas, Fréchet, Popoviciu, polynomials, monomials, p -Wright affine functions, and others. also how to use study approximate eigenvalues eigenvectors some operators.