Classical Approximations of Multiplicative Inverse Type Septendecic and Octadecic Functional Equations in Quasi-$$\beta $$-normed Spaces

2020 ◽  
pp. 45-55
Author(s):  
B. V. Senthil Kumar ◽  
Hemen Dutta
Keyword(s):  
Functional Equations ◽  
Normed Spaces ◽  
Multiplicative Inverse

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 Hyers-Ulam stability of quadratic forms in 2-normed spaces

2019 ◽  
Vol 52 (1) ◽  
pp. 496-502
Author(s):  
Won-Gil Park ◽  
Jae-Hyeong Bae
Keyword(s):  
Banach Spaces ◽  
Quadratic Forms ◽  
Functional Equations ◽  
Ulam Stability ◽  
Normed Spaces

AbstractIn this paper, we obtain Hyers-Ulam stability of the functional equationsf (x + y, z + w) + f (x − y, z − w) = 2f (x, z) + 2f (y, w),f (x + y, z − w) + f (x − y, z + w) = 2f (x, z) + 2f (y, w)andf (x + y, z − w) + f (x − y, z + w) = 2f (x, z) − 2f (y, w)in 2-Banach spaces. The quadratic forms ax2 + bxy + cy2, ax2 + by2 and axy are solutions of the above functional equations, respectively.

scholarly journals Additive ρ-functional inequalities in β-homogeneous normed spaces

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1651-1658
Author(s):  
Choonkil Park
Keyword(s):  
Banach Spaces ◽  
Complex Number ◽  
Functional Equations ◽  
Additive Functional ◽  
Functional Inequalities ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Homogeneous Complex ◽  
Fixed Complex

In this paper, we solve the following additive ?-functional inequalities ||f (x + y) - f (x) - f (y)|| ? ???(2f (x+y/2) - f(x) + -f (y))??, (1) where ? is a fixed complex number with |?|<1, and ??2f(x+y/2)-f(x)- f(y)???||?(f(x+y)-f(x)-f(y))||, (2) where ? is a fixed complex number with |?|<1/2 , and prove the Hyers-Ulam stability of the additive ?-functional inequalities (1) and (2) in ?-homogeneous complex Banach spaces and prove the Hyers-Ulam stability of additive ?-functional equations associated with the additive ?-functional inequalities (1) and (2) in ?-homogeneous complex Banach spaces.

scholarly journals Hyers–Ulam–Rassias Stability of Additive Mappings in Fuzzy Normed Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Jianrong Wu ◽  
Lingxiao Lu
Keyword(s):  
Functional Equations ◽  
Normed Spaces ◽  
Additive Mappings ◽  
Rassias Stability

In this paper, the Hyers–Ulam–Rassias stabilities of two functional equations, f a x + b y = r f x + s f y and f x + y + z = 2 f x + y / 2 + f z , are investigated in the framework of fuzzy normed spaces.

scholarly journals On the probabilistic stability of some functional equations

2013 ◽  
Vol 29 (1) ◽  
pp. 125-132
Author(s):  
CLAUDIA ZAHARIA ◽  
◽  
DOREL MIHET ◽  
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Stability Of Functional Equations ◽  
The Stability ◽  
Stability Results

We establish stability results concerning the additive and quadratic functional equations in complete Menger ϕ-normed spaces by using fixed point theory. As particular cases, some theorems regarding the stability of functional equations in β - normed and quasi-normed spaces are obtained.

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.

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