On solvable operators which imply the general solution of a polygonal functional equation on the real plane

2004 ◽  
Vol 67 (1-2) ◽  
pp. 169-174
Author(s):  
Shigeru Haruki ◽  
Shin-ichi Nakagiri
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Real Plane ◽  
The Real

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.

A fixed point approach to the stability of sextic Lie *-derivations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4933-4944
Author(s):  
Dongseung Kang ◽  
Heejeong Koh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Single Case ◽  
Fixed Point Method ◽  
Point Method ◽  
Fixed Point Approach ◽  
The Stability ◽  
The Given ◽  
Lie Derivations

We obtain a general solution of the sextic functional equation f (ax+by)+ f (ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)] + 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.

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.

Level curves of open polynomial functions on the real plane

1994 ◽  
Vol 22 (14) ◽  
pp. 5973-5981
Author(s):  
J. Ferrera ◽  
M.J. de la Puente
Keyword(s):  
Real Plane ◽  
Polynomial Functions ◽  
The Real ◽  
Level Curves

Modal logics of domains on the real plane

Studia Logica ◽  
1983 ◽  
Vol 42 (1) ◽  
pp. 63-80 ◽  
Author(s):  
V. B. Shehtman
Keyword(s):  
Modal Logics ◽  
Real Plane ◽  
The Real

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.

Continuous Solutions of the Functional Equation fn(x) = f(x)

1953 ◽  
Vol 5 ◽  
pp. 101-103 ◽  
Author(s):  
G. M. Ewing ◽  
W. R. Utz
Keyword(s):  
Functional Equation ◽  
Real Axis ◽  
Continuous Solutions ◽  
The Real ◽  
Real Functions ◽  
Image Position

In this note the authors find all continuous real functions defined on the real axis and such that for an integer n > 2, and for each x,

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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