Stability and instability of multi-quadratic reciprocal functions

In this investigation, we introduce a multi-quadratic reciprocal function as a system of quadratic reciprocal functional equations and obtain the general solution of such systems. Moreover, we establish some known (Hyers, Găvruţa and Rassias) stability results of multi-quadratic reciprocal functions on nonzero real numbers as a pointwise stability. Furthermore, by means of a characterization of multi-quadratic reciprocal functions, we give a non-stable example of a multi-quadratic reciprocal function in the singularity case. Applying a rational form of the inverse quadratic functional equation, we introduce a novel multi-quadratic reciprocal function as a general system of multi-quadratic reciprocal functional equations which is different from the previous studies. Then, we demonstrate an representation of such system of functional equations as an unified equation. Lastly, by using a single functional inequality, we explore the stability of multi-quadratic reciprocal functions.