We propose the concept of orthogonally triangular $\alpha$-admissible mapping and demonstrate some fixed point theorems for self-mappings in orthogonal complete metric spaces. Some of the well-known outcomes in the literature are generalized and expanded by our results. An instance to help our outcome is presented. We also explore applications of our key results.

In this paper, we introduce the concept of hyper homomorphisms and hyper derivations in Banach algebras and we establish the stability of hyper homomorphisms and hyper derivations in Banach algebras for the following 3-additive functional equation:

$$\begin{array}{r}g(x_1+x_2,y_1+y_2,z_1+z_2)=\sum _{i,j,k=1}^{2}g(x_i,y_j,z_k).\end{array}$$

The main aim of this paper is to investigate various types of Hyers-Ulam stability of linear differential equations of $n^{th}$ order with constant coefficients using the Mahgoub transform method. We also show the Hyers-Ulam constants of these differential equations and give some main results.