and Applied Analysis 3 Theorem 1.2 Rassias 18 . Let X be a real normed linear space and Y a real complete normed linear space. Assume that f : X → Y is an approximately additive mapping for which there exist constants θ ≥ 0 and p, q ∈ R such that r p q / 1 and f satisfies the inequality ∥ ∥f ( x y ) − f x − f(y)∥∥ ≤ θ‖x‖p∥∥y∥∥q 1.5 for all x, y ∈ X. Then there exists a unique additive mapping L...

Herein, we mainly employ the fixed point theorem and Lax-Milgram in functional analysis to prove existence uniqueness of generalized mixed finite element (MFE) solutions for two-dimensional steady Boussinesq equation. Thus, can fill gap research equation since existing studies are assumed solution without providing proof.

This paper deals with the existence and uniqueness of the classical solution of Fourier’s first problem for a wide class of systems of two weakly coupled quasi-linear second order partial differential functional equations. One equation is of the parabolic type (the degenerated parabolic equation) and the other of the elliptic type (the elliptic equation with a parameter). The functional depende...