Stability Analysis of A Hotel Model And Assessment Using Additive Functional Equations

This paper introduces a new class of systems of additive functional equations

H_K(p_K+ r_K+ f_K+q_K1+ q_K2+ s_K+t_K) = H_K(p_K)+ H_K(r_K)+ H_K(f_K)+ H_K(q_K1)+ H_K(q_K2)+ H_K(s_K)+ H_K(t_K)

including parking availability, restroom facilities, food services, and service-related factors.

This provides a concrete applied framework that connects abstract functional equations with real-world modeling. The primary aim of the study is to establish the Ulam–Hyers (UH) stability of the proposed class of equations in complete normed linear spaces. To achieve this, a general control function is employed in conjunction with sumpowers of norms, product, powers of norms and mixed product-sum expressions involving powers of norms. Using a direct analytical approach, explicit stability conditions are derived for each functional equation considered. One of the significant contributions of this work lies in the introduction of multiple interrelated functional equations and the unified treatment of their stability analysis. Furthermore, an application is presented to demonstrate the practical significance of the theoretical results. A comparative discussion is also included to highlight the consistency of the results with established stability analyses and supporting mathematical computations.

All abbreviations are properly defined, and the equations are expressed in clear mathematical form to ensure readability and precision.