Reciprocal Functional Equation Research Articles

Stability Analysis of l-Power Reciprocal Functional Equation in Intuitionistic Fuzzy Banach Spaces

In this study, we explore the generalized Hyers-Ulam-Rassias stability of a l-power reciprocal functional equation in Intuitionistic Fuzzy Banach Spaces.

Further Stability Results of the Functional Equation in Non-Archimedean Space

In this paper, we investigate the generalized Hyers-Ulam stability of the following reciprocal functional equation in non-Archimedean space using a direct method.

Stabilities and Non-Stabilities of a New Reciprocal Functional Equation

Abstract The intention of this study is to present some stronger results by investigating Ulam-JRassias product stability and Ulam-JRassias mixed-type sum-product stability of a new reciprocal functional equation. Also, a suitable counter-example is presented to show the failure of stability result for the singular case.

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

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_{mathrm{eq}} of parallel electrical circuit using functional equations, which relates the electrical resistances and conductances with suitable examples.

Hyperstability of Rassias-Ravi reciprocal functional equation

Hyperstability of Rassias-Ravi reciprocal functional equation

On the Stability of the Functional Equation f(2x+y)+f(x+y2)=2f(x)f(y)f(x)+f(y)+2f(x+y)f(y-x)3f(y-x)-f(x+y)f\left( {2x + y} \right) + f\left( {{{x + y} \over 2}} \right) = {{2f\left( x \right)f\left( y \right)} \over {f\left( x \right) + f\left( y \right)}} + {{2f\left( {x + y} \right)f\left( {y - x} \right)} \over {3f\left( {y - x} \right) - f\left( {x + y} \right)}}

Abstract The aim of this paper is to obtain the general solution to a reciprocal functional equation of the form f ( 2 x + y ) + f ( x + y 2 ) = 2 f ( x ) f ( y ) f ( x ) + f ( y ) + 2 f ( x + y ) f ( y - x ) 3 f ( y - x ) - f ( x + y ) f\left( {2x + y} \right) + f\left( {{{x + y} \over 2}} \right) = {{2f\left( x \right)f\left( y \right)} \over {f\left( x \right) + f\left( y \right)}} + {{2f\left( {x + y} \right)f\left( {y - x} \right)} \over {3f\left( {y - x} \right) - f\left( {x + y} \right)}} and to investigate its generalized Hyers-Ulam-Rassias stability.

Approximation of Jensen type reciprocal functional equation using fixed point technique

In this study, we propose a new rational functional equationJr((x+y)/2)=2Jr(x)Jr(y)/[Jr(x)+Jr(y)]and obtain its solution. We also investigate its various stabilities by a fixed point method

Non-archimedean stability and non-stability of quadratic reciprocal functional equation in several variables

Non-archimedean stability and non-stability of quadratic reciprocal functional equation in several variables

Ulam-Hyers stability of quadratic reciprocal functional equation in intuitionistic random normed spaces: Various methods

In this paper, the authors investigated the intuitionistic random stability of a quadratic reciprocal functional equation$$f(x+2 y)+f(2 x+y)=\frac{f(x) f(y)[5 f(x)+5 f(y)+8 \sqrt{f(x) f(y)}]}{[2 f(x)+2 f(y)+5 \sqrt{f(x)+f(y)}]^2}$$using direct and fixed point methods.

Generalized Hyers-Ulam Stability of a Cubic Reciprocal Functional Equation

Generalized Hyers-Ulam Stability of a Cubic Reciprocal Functional Equation

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

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.

Erratum to: Approximation on the reciprocal functional equation in several variables in matrix non-Archimedean random normed spaces

Erratum to: Approximation on the reciprocal functional equation in several variables in matrix non-Archimedean random normed spaces

Approximation on the reciprocal functional equation in several variables in matrix non-Archimedean random normed spaces

In this paper, we investigate the generalized Hyers-Ulam stability of a reciprocal type functional equation in several variables in matrix non-Archimedean random normed spaces by direct and fixed point methods.

Approximation on the Quadratic Reciprocal Functional Equation

The quadratic reciprocal functional equation is introduced. The Ulam stability problem for anϵ-quadratic reciprocal mappingf:X→Ybetween nonzero real numbers is solved. The Găvruţa stability for the quadratic reciprocal functional equations is established as well.

ON THE STABILITY OF THE GENERALIZED G-TYPE FUNCTIONAL EQUATIONS

In this paper, we obtain the generalization of the Hyers-Ulam-Rassias stability in the sense of Gavruta and Ger of the generalized G-type functional equations of the form <TEX>$f({{\varphi}(x)) = {\Gamma}(x)f(x)$</TEX>. As a consequence in the cases <TEX>${\varphi}(x) := x+p:= x+1$</TEX>, we obtain the stability theorem of G-functional equation : the reciprocal functional equation of the double gamma function.