K. Ravi

Mixed Type Of Additive And Quintic Functional Equations

Abstract In this paper, we investigate the general solution and Hyers–Ulam–Rassias stability of a new mixed type of additive and quintic functional equation of the form f(3x+y)−5f(2x+y)+f(2x−y)+10f(x+y)−5f(x−y)=10f(y)+4f(2x)−8f(x)

Ulam-Hyers Stability of Euler-Lagrange-Jensen- (a,b)-Sextic Functional Equations in Quasi-𝛽- Normed Spaces

f\left( {3x + y} \right) - 5f\left( {2x + y} \right) + f\left( {2x - y} \right) + 10f\left( {x + y} \right) - 5f\left( {x - y} \right) = 10f\left( y \right) + 4f\left( {2x} \right) - 8f\left( x \right)

n-dimensional quintic and sextic functional equations and their stabilities in Felbin type spaces

in the set of real numbers.

STABILITY OF A GENERALIZED MIXED TYPE ADDITIVE, QUADRATIC, CUBIC AND QUARTIC FUNCTIONAL EQUATION

Abstract In this study, we achieve the general solution and investigate Ulam-Hyers stabilities involving a general control function, sum of powers of norms, product of powers of norms and mixed product-sum of powers of norms of the duodecic functional equation in quasi-β-normed spaces via fixed point method. We also illustrate a counter-example for non-stability of the duodecic functional equation in singular case.

ULAM STABILITY OF RECIPROCAL DIFFERENCE AND ADJOINT FUNCTIONAL EQUATIONS

The purpose of this paper is to prove various stabilities of the following Euler-Lagrange-Jensen-(a, b)-sextic functional equation f(ax + by) + f(bx + ay) +(a − b) [f ( ax − by a − b ) + f ( bx − ay b − a )] = 64(ab)(a + b) [f ( x+y 2 ) + f ( x−y 2 )] +2(a − b)(a − b)[f(x) + f(y)] where a ≠ b, such that μ ∈ R; μ = a + b ≠ 0,±1 and λ = 1 + (a − b) − 2(a + b) − 62(ab)(a + b) ≠ 0, in quasi-βnormed spaces by considering ‘control function φ(x, y)’, a constant ‘θ’, ‘sum of powers of norms’, ‘product of powers of norms’ and ‘mixed product-sum of different powers of norms’ as upper bounds using direct method.

Ulam Stability of Generalized Reciprocal Functional Equation in Several Variables

Abstract In this paper, we acquire the general solution of the undecic functional equation f(x + 6y) - 11f(x + 5y) + 55f(x + 4y) - 165f(x + 3y) + 330f(x + 2y) - 462f(x + y) + 462f(x) - 330f(x - y) + 165f(x - 2y) - 55f(x - 3y) + 11f(x - 4y) - f(x - 5y) = 39916800f(y). We also obtain the generalized Ulam-Hyers stability of the above functional equation in quasi- β-normed spaces using fixed point method. Moreover, we investigate the pertinent stabilities of the above functional equation using sum of powers of norms, product of powers of norms and mixed product-sum of powers of norms as upper bounds. We also present a counter-example for non-stability of the above functional equation in singular case.

Solution and stability of a reciprocal type functional equation in several variables

Abstract In this paper, we derive general solution of new n-dimensional quintic and sextic functional equations and investigate the Hyers–Ulam stability, Hyers–Ulam–Rassias stability and generalized Hyers–Ulam–Rassias stability for quintic and sextic functional equations in Felbin type fuzzy normed linear spaces. Also, we give the counter examples for the Hyers–Ulam–Rassias stability of quintic and sextic functional equations for some cases.