Reciprocal squared functional inequalities and equations

There are many interesting solutions and exceptional applications of linear functional inequalities and equations in optimization theory to define convex sets and convex functions, probability theory to study the properties of probability distributions, such as their spread or moments and analysis to estimate eigenvalues and eigenfunctions of operators. Inspired through the significant role of linear functional inequalities and equations, this paper proposes two novel reciprocal squared functional inequalities and equations. First, we obtain the solutions of these reciprocal squared functional inequalities and equations. An interesting feature of these inequalities and equations is that they have reciprocal squared functions as their solutions. Further, we provide solutions to the stability problems of these reciprocal squared functional inequalities with different upper bounds in the space of complex numbers using the method devised by Hyers (direct method). Finally, we show that the findings of this study differ from those of previously published results via a comparison study.