scholarly journals Functional equation and its modular stability with and without Δp-condition

Filomat ◽  
2020 ◽  
Vol 34 (3) ◽  
pp. 919-930
Author(s):  
Murali Ramdoss ◽  
Divyakumari Pachaiyappan ◽  
Hemen Dutta
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Modular Space ◽  
Fatou Property

Mixed type is a further step of development in functional equations. In this paper, the authors made an attempt to introduce such equation of the following form with its general solution h(py + z) + h(py-z) + h(y + pz) + h(y-pz) = (p + p2)[h(y + z) + h(y-z)] + 2h(py)- 2(p2 + p-1)h(y) for all y,z ? R, p ? 0,?1. Also, without Fatou property authors investigate its various stabilities related to Ulam problem in modular space by considering with and without ?p-condition.

Solutions and Stability of Generalized Mixed Type QCA-Functional Equations in Random Normed Spaces

2013 ◽  
Vol 59 (2) ◽  
pp. 299-320
Author(s):  
M. Eshaghi Gordji ◽  
Y.J. Cho ◽  
H. Khodaei ◽  
M. Ghanifard
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Probabilistic Normed Spaces ◽  
Random Normed Spaces ◽  
Generalized Stability

Abstract In this paper, we investigate the general solution and the generalized stability for the quartic, cubic and additive functional equation (briefly, QCA-functional equation) for any k∈ℤ-{0,±1} in Menger probabilistic normed spaces.

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

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
K. Tamilvanan ◽  
Nazek Alessa ◽  
K. Loganathan ◽  
G. Balasubramanian ◽  
Ngawang Namgyel
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Normed Space ◽  
Functional Equations ◽  
Mixed Type ◽  
Research Area ◽  
Quadratic Functional ◽  
Research Papers ◽  
The Stability ◽  
Stability Results

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).

scholarly journals Mixed Type Of Additive And Quintic Functional Equations

2015 ◽  
Vol 29 (1) ◽  
pp. 35-50 ◽  
Author(s):  
Abasalt Bodaghi ◽  
Pasupathi Narasimman ◽  
Krishnan Ravi ◽  
Behrouz Shojaee
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Real Numbers ◽  
Rassias Stability

AbstractIn 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 $$f\left( {3x + y} \right) - 5f\left( {2x + y} \right) + f\left( {2x - y} \right) + 10f\left( {x + y} \right) - 5f\left( {x - y} \right) = 10f\left( y \right) + 4f\left( {2x} \right) - 8f\left( x \right)$$ in the set of real numbers.

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 The new investigation of the stability of mixed type additive-quartic functional equations in non-Archimedean spaces

2020 ◽  
Vol 53 (1) ◽  
pp. 174-192
Author(s):  
Anurak Thanyacharoen ◽  
Wutiphol Sintunavarat
Keyword(s):  
Functional Equation ◽  
Normed Space ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Group ◽  
Ulam Stability ◽  
Quartic Functional Equation ◽  
The Stability

AbstractIn this article, we prove the generalized Hyers-Ulam stability for the following additive-quartic functional equation:f(x+3y)+f(x-3y)+f(x+2y)+f(x-2y)+22f(x)+24f(y)=13{[}f(x+y)+f(x-y)]+12f(2y),where f maps from an additive group to a complete non-Archimedean normed space.

scholarly journals Solution and Stability of a Mixed Type Cubic and Quartic Functional Equation in Quasi-Banach Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
S. Zolfaghari ◽  
J. M. Rassias ◽  
M. B. Savadkouhi
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Banach Spaces ◽  
Mixed Type ◽  
Quartic Functional Equation

We obtain the general solution and the generalized Ulam-Hyers stability of the mixed type cubic and quartic functional equationf(x+2y)+f(x−2y)=4(f(x+y)+f(x−y))−24f(y)−6f(x)+3f(2y)in quasi-Banach spaces.

scholarly journals Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non-Archimedean Normed Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Abasalt Bodaghi ◽  
Sang Og Kim
Keyword(s):  
Functional Equation ◽  
Positive Integer ◽  
General Solution ◽  
Functional Equations ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Additive Functions ◽  
Normed Spaces

We obtain the general solution of the generalized mixed additive and quadratic functional equationfx+my+fx−my=2fx−2m2fy+m2f2y,mis even;fx+y+fx−y−2m2−1fy+m2−1f2y,mis odd, for a positive integerm. We establish the Hyers-Ulam stability for these functional equations in non-Archimedean normed spaces whenmis an even positive integer orm=3.

scholarly journals Approximate Quartic and Quadratic Mappings in Quasi-Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-18
Author(s):  
M. Eshaghi Gordji ◽  
H. Khodaei ◽  
Hark-Mahn Kim
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Banach Spaces ◽  
Mixed Type ◽  
Quadratic Mapping ◽  
Ulam Stability ◽  
Linear Spaces ◽  
Quadratic Mappings

we establish the general solution for a mixed type functional equation of aquartic and a quadratic mapping in linear spaces. In addition, we investigate the generalized Hyers-Ulam stability inp-Banach spaces.

scholarly journals Solution and Hyers-Ulam-Rassias Stability of Generalized Mixed Type Additive-Quadratic Functional Equations in Fuzzy Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
H. Azadi Kenary ◽  
H. Rezaei ◽  
Y. W. Lee ◽  
G. H. Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Functional Equations ◽  
Mixed Type ◽  
Direct Method ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Fixed Point Methods ◽  
Rassias Stability

By using fixed point methods and direct method, we establish the generalized Hyers-Ulam stability of the following additive-quadratic functional equationf(x+ky)+f(x−ky)=f(x+y)+f(x−y)+(2(k+1)/k)f(ky)−2(k+1)f(y)for fixed integerskwithk≠0,±1in fuzzy Banach spaces.

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