Stability results of the functional equation deriving from quadratic function in random normed spaces

The investigation of the stabilities of various types of equations is an interesting and evolving research area in the field of mathematical analysis. Recently, there are many research papers published on this topic, especially additive, quadratic, cubic, and mixed type functional equations. We propose a new functional equation in this study which is quite different from the functional equations already dealt in the literature. The main feature of the equation dealt in this study is that it has three different solutions, namely, additive, quadratic, and mixed type functions. We also prove that the stability results hold good for this equation in intuitionistic random normed space (briefly, IRN-space).

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“…, 0,⋯,0Þ in (18), we obtain φð0Þ = 0. Interchanging ðv 1 , v 2 ,⋯,v m Þ with ðv, 0, 0,⋯,0Þ in (18), we obtain…”

Section: Solution Of the Functional Equation (3)mentioning

confidence: 87%

“…For additional information regard-ing the outcomes about such issues, the related background in [6][7][8][9][10][11][12] can be examined. Absorbing new outcomes concerning mixed-type functional equations has as of late been acquired by Najati et al [13][14][15], Jun and Kim [16,17], and Park [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

General Solution and Stability of Additive-Quadratic Functional Equation in IRN-Space

Tamilvanan¹,

Alessa

Loganathan³

et al. 2021

Journal of Function Spaces

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“…We adopt the usual terminology, notions and conventions of the theory of random normed spaces as in [14].…”

Section: Original Research Articlementioning

confidence: 99%

Hyer-Ulam-Stability of Generalized Quadratic Functional Equation in Random Normed Spaces

Devi

2023

ARJOM

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“…Next is to determine the solution at the second-order stage and the expressions of heat and mass transport in terms of Nusselt number Nu and Sherwood numbers Sh i and equate the coefficient of 2 in Equation (30) and then obtain the following equations.…”

Section: Second-order Solutionmentioning

confidence: 99%

Dynamics of Newtonian Liquids with Distinct Concentrations Due to Time-Varying Gravitational Acceleration and Triple Diffusive Convection: Weakly Non-Linear Stability of Heat and Mass Transfer

et al. 2023

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One of the practical methods for examining the stability and dynamical behaviour of non-linear systems is weakly non-linear stability analysis. Time-varying gravitational acceleration and triple-diffusive convection play a significant role in the formation of acceleration, inducing some dynamics in the industry. With an emphasis on the natural Rayleigh–Bernard convection, more is needed on the significance of a modulated gravitational field on the heat and mass transfer due to triple convection focusing on weakly non-linear stability analysis. The Newtonian fluid layers were heated, salted and saturated from below, causing the bottom plate’s temperature and concentration to be greater than the top plate’s. In this study, the acceleration due to gravity was assumed to be time-dependent and comprised of a constant gravity term and a time-dependent gravitational oscillation. More so, the amplitude of the modulated gravitational field was considered infinitesimal. The case in which the fluid layer is infinitely expanded in the x-direction and between two concurrent plates at z=0 and z=d was considered. The asymptotic expansion technique was used to retrieve the solution of the Ginzburg–Landau differential equation (i.e., a system of non-autonomous partial differential equations) using the software MATHEMATICA 12. Decreasing the amplitude of modulation, Lewis number, Rayleigh number and frequency of modulation has no significant effect on the Nusselt number proportional to heat-transfer rates (Nu), Sherwood number proportional to mass transfer of solute 1 (Sh1) and Sherwood number proportional to mass transfer of solute 2 (Sh2) at the initial time. The crucial Rayleigh number rises in value in the presence of a third diffusive component. The third diffusive component is essential in delaying the onset of convection.

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Stability results of the functional equation deriving from quadratic function in random normed spaces

Abstract: <abstract> <p>The authors introduce a finite variable quadratic functional equation and derive its solution. Also, authors examine its Hyers-Ulam stability in Random Normed space(RN-space) by means of two different methods.</p> </abstract>

Cited by 8 publications

References 18 publications

General Solution and Stability of Additive-Quadratic Functional Equation in IRN-Space

General Solution and Stability of Additive-Quadratic Functional Equation in IRN-Space

Hyer-Ulam-Stability of Generalized Quadratic Functional Equation in Random Normed Spaces

Dynamics of Newtonian Liquids with Distinct Concentrations Due to Time-Varying Gravitational Acceleration and Triple Diffusive Convection: Weakly Non-Linear Stability of Heat and Mass Transfer

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