scholarly journals Modular Stabilities of a Reciprocal Second Power Functional Equation

2020 ◽  
Vol 13 (5) ◽  
pp. 1162-1175
Author(s):  
B. V. Senthil Kumar ◽  
Hemen Dutta ◽  
S. Sabarinathan
Keyword(s):  
Functional Equation ◽  
Electrostatic Forces ◽  
Fatou Property ◽  
Rational Form ◽  
Modular Spaces

In the present work, we propose a dierent reciprocal second power Functional Equation (FE) which involves the arguments of functions in rational form and determine its stabilities in the setting of modular spaces with and without using Fatou property. We also prove the stabilities in beta-homogenous spaces. As an application, we associate this equation with the electrostatic forces of attraction between unit charges in various cases using Coloumb's law.

scholarly journals Two multi-cubic functional equations and some results on the stability in modular spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Choonkil Park ◽  
Abasalt Bodaghi
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Modular Function ◽  
Modular Space ◽  
Fatou Property ◽  
Cubic Functional Equation ◽  
Mild Conditions ◽  
Modular Spaces ◽  
The Stability

AbstractIn this article, we study n-variable mappings which are cubic in each variable. We also show that such mappings can be described by an equation, say, multi-cubic functional equation. Furthermore, we study the stability of such functional equations in the modular space $X_{\rho }$Xρ by applying $\Delta _{2}$Δ2-condition and the Fatou property (in some cases) on the modular function ρ. Finally, we show that, under some mild conditions, one of these new multi-cubic functional equations can be hyperstable.

scholarly journals Stability of a generalized n-variable mixed-type functional equation in fuzzy modular spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Murali Ramdoss ◽  
Divyakumari Pachaiyappan ◽  
Choonkil Park ◽  
Jung Rye Lee
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Research Paper ◽  
Fixed Point Method ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Modular Spaces

AbstractThis research paper deals with general solution and the Hyers–Ulam stability of a new generalized n-variable mixed type of additive and quadratic functional equations in fuzzy modular spaces by using the fixed point method.

scholarly journals Stability of an additive-quartic functional equation in modular spaces

2021 ◽  
Vol 26 (01) ◽  
pp. 22-40
Author(s):  
S. Karthikeyan ◽  
C. Park ◽  
P. Palani ◽  
T. R. K. Kumar
Keyword(s):  
Functional Equation ◽  
Modular Spaces ◽  
Quartic Functional Equation

scholarly journals Stability of an n-variable mixed type functional equation in probabilistic modular spaces

2020 ◽  
Vol 5 (6) ◽  
pp. 5903-5915
Author(s):  
Murali Ramdoss ◽  
◽  
Divyakumari Pachaiyappan ◽  
Inho Hwang ◽  
Choonkil Park ◽  
...  
Keyword(s):  
Functional Equation ◽  
Mixed Type ◽  
Modular Spaces

On the generalized orthogonal stability of the pexiderized quadratic functional equations in modular spaces

2017 ◽  
Vol 67 (1) ◽  
Author(s):  
Iz-iddine EL-Fassi ◽  
Samir Kabbaj
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Modular Spaces ◽  
Generalized Orthogonal ◽  
Rassias Stability

AbstractIn this paper, we establish the Hyers-Ulam-Rassias stability of the quadratic functional equation of Pexiderized type

scholarly journals A Best Proximity Point Result in Modular Spaces with the Fatou Property

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Mohamed Jleli ◽  
Erdal Karapınar ◽  
Bessem Samet
Keyword(s):  
Existence And Uniqueness ◽  
Best Proximity Point ◽  
Sufficient Conditions ◽  
Modular Space ◽  
Fatou Property ◽  
Best Proximity Points ◽  
Modular Spaces

Consider a nonself-mapping , where is a pair of nonempty subsets of a modular space . A best proximity point of is a point satisfying the condition: . In this paper, we introduce the class of proximal quasicontraction nonself-mappings in modular spaces with the Fatou property. For such mappings, we provide sufficient conditions assuring the existence and uniqueness of best proximity points.

A Fixed Point Approach to the Stability of Quadratic Functional Equations in Modular Spaces

2017 ◽  
Vol 6 (1) ◽  
pp. 171-175
Author(s):  
Seong Sik Kim ◽  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Quadratic Functional ◽  
Fixed Point Approach ◽  
Modular Spaces ◽  
The Stability ◽  
Positive Integers ◽  
Rassias Stability

In this paper, we investigate the generalized Hyers-Ulam-Rassias stability of the following quadratic functional equation f(kx + y) + f(kx – y) = 2k2f(x) + 2f(y) for any fixed positive integers k ∈ Ζ+ in modular spaces by using fixed point method.

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