On One Method for Solving a Mixed Boundary Value Problem for a Parabolic Type Equation Using Operators \(\mathbb{A}{{\mathbb{T}}_{{\lambda ,j}}}\)

The paper proposes a new method for obtaining a generalized solution to the mixed boundary value problem for a parabolic equation with boundary conditions of the third kind and a continuous initial condition. Generalized functions are understood in the sense of the sequential approach. The representative of the class of sequences, which is a generalized function, is obtained using the function interpolation operator, constructed using solutions to the Cauchy problem. The solution is obtained in the form of a series that converges uniformly inside the domain of the solution.