Author:
Nawaz Sundas,Bariq Abdul,Batool Afshan,Akgül Ali
Abstract
AbstractIn our research work generalized Hyers-Ulam stability of the following functional inequalities is analyzed by using fixed point approach: $$\begin{aligned}& \biggl\Vert f(2x+y)+f(2x-y)-2f(x+y)-2f(x-y)-12f(x) \\& \quad {}-\rho \biggl(4f\biggl(x+\frac{y}{2}\biggr)+4\biggl(f\biggl(x- \frac{y}{2}\biggr)-f(x+y)-f(x-y)\biggr)-6f(x),r\biggr) \biggr\Vert \geq \frac{r}{r+\varphi (x, y)} \end{aligned}$$
∥
f
(
2
x
+
y
)
+
f
(
2
x
−
y
)
−
2
f
(
x
+
y
)
−
2
f
(
x
−
y
)
−
12
f
(
x
)
−
ρ
(
4
f
(
x
+
y
2
)
+
4
(
f
(
x
−
y
2
)
−
f
(
x
+
y
)
−
f
(
x
−
y
)
)
−
6
f
(
x
)
,
r
)
∥
≥
r
r
+
φ
(
x
,
y
)
and $$\begin{aligned}& \biggl\Vert f(2x+y)+f(2x-y)-4f(x+y)-4f(x-y)-24f(x)+6f(y) \\& \qquad {}-\rho \biggl(8f\biggl(x+\frac{y}{2}\biggr)+8\biggl(f\biggl(x- \frac{y}{2}\biggr)-2f(x+y)-2f(x-y)\biggr)-12f(x)+3f(y),r\biggr) \biggr\Vert \\& \quad \geq \frac{r}{r+\varphi (x, y)} \end{aligned}$$
∥
f
(
2
x
+
y
)
+
f
(
2
x
−
y
)
−
4
f
(
x
+
y
)
−
4
f
(
x
−
y
)
−
24
f
(
x
)
+
6
f
(
y
)
−
ρ
(
8
f
(
x
+
y
2
)
+
8
(
f
(
x
−
y
2
)
−
2
f
(
x
+
y
)
−
2
f
(
x
−
y
)
)
−
12
f
(
x
)
+
3
f
(
y
)
,
r
)
∥
≥
r
r
+
φ
(
x
,
y
)
in the setting of fuzzy matrix, where $\rho \neq 2$
ρ
≠
2
is a real number.We also discussed Hyers-Ulam stability from the application point of view.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference57 articles.
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