Ulam - Hyers stability of a 2- variable AC - mixed type functional equation in quasi - beta normed spaces: direct and fixed point methods

Rassias, John Michael; Arunkumar, M.; Ramamoorthi, S.; Hemalatha, S.

doi:10.26637/mjm202/003

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“…in Banach spaces [3] and Quasi-Beta normed space [21]. Following the same approach, in this paper, we investigate the general solution and establish that generalized Ulam-Hyers stability of the 2-variable k-AC mixed type functional equation…”

Section: Introductionmentioning

confidence: 99%

On the probabilistic stability of the 2-variable k-AC-mixed type functional equation

et al. 2016

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Section: Introductionmentioning

confidence: 99%

On the probabilistic stability of the 2-variable k-AC-mixed type functional equation

et al. 2016

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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)}}

Sadani

2020

Tatra Mountains Mathematical Publications

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The aim of this paper is to obtain the general solution to a reciprocal functional equation of the formf\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.

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Ulam - Hyers stability of a 2- variable AC - mixed type functional equation in quasi - beta normed spaces: direct and fixed point methods

Abstract: In this paper, we obtain the generalized Ulam - Hyers stability of a 2 - variable AC - mixed type functional equation$$f(2 x+y, 2 z+w)-f(2 x-y, 2 z-w)=4[f(x+y, z+w)-f(x-y, z-w)]-6 f(y, w)$$in Quasi - Beta normed space using direct and fixed point methods.

Cited by 2 publications

References 23 publications

On the probabilistic stability of the 2-variable k-AC-mixed type functional equation

On the probabilistic stability of the 2-variable k-AC-mixed type functional equation

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