On the stability of quadratic reciprocal functional equation in non-Archimedean fields

Abstract

In this paper, we introduce a new form of the quadratic reciprocal functional equation. Then, we study the Hyers–Ulam stability for this quadratic reciprocal functional equation in non-Archimedean fields.

Stabilities and non-stabilities of reciprocal-nonic and reciprocal-decic functional equations

“…for all x, y, t ∈ N. The equations (1.2) and (1.3) are applied to remove noise in an image by filtering techniques. The study of stability of several functional equations in various spaces and their solutions as rational functions can be found in [2], [3], [4], [5], [6], [7], [12], [15], [16], [17], [21], [22], [26], [27], [28].…”

Approximation of multiplicative inverse undecic and duodecic functional equations

“…There are many significant and remarkable results concerning the stability of different forms of functional equations, one can refer to the studies of Jung, Mirmostafaee, and Park, Shin, Saadati, and Lee. ()…”

Approximation of Reciprocal-Cubic Functional Equation in Non-Archimedean Normed Space

“…If every Cauchy sequence in X converges, then the non-Archimedean normed space X is called a non-Archimedean Banach space. Throughout this paper, we consider that X and Y are a non-Archimedean field and a complete non-Archimedean field, respectively.Let us define the function by (6) for all . Also let us assume numerator and denominator of equation is non zero for all and .…”