Relation between electrical resistance and conductance using multifarious functional equations and applications to parallel circuit

Abstract

Abstract In this paper, we introduce a new generalized p-dimensional multifarious radical reciprocal functional equation combining three classical means: arithmetic, geometric, and harmonic. Mainly, we find its general solution and stability related to the Ulam problem in modular spaces by using the fixed point method with suitable counterexamples. Importantly, in this paper, we illustrate the geometrical interpretation and applications of the introduced Pythagorean means multifarious functional equation in connection with the parallel circuit. Furthermore, we provide a formula for finding the equivalent resistance R eq $R_{\mathrm{eq}}$ of parallel electrical circuit using functional equations, which relates the electrical resistances and conductances with suitable examples.

Keywords

• Hyers–Ulam stability
• Functional equation
• Fixed point method
• Fuzzy modular space