In the present paper, we develop some implications leading to Carathéodory functions in the open disk and provide some new conditions for functions to be p-valent functions. This work also extends ...the findings of Nunokawa and others.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
In this paper, the basic theory for the initial value problems for fractional functional differential equations is considered, extending the corresponding theory of ordinary functional differential ...equations.
The analysis of stability in functional equations (FEs) within neutrosophic normed spaces is a significant challenge due to the inherent uncertainties and complexities involved. This paper proposes a ...novel approach to address this challenge, offering a comprehensive framework for investigating stability properties in such contexts. Neutrosophic normed spaces are a generalization of traditional normed spaces that incorporate neutrosophic logic. By providing a systematic methodology for addressing stability concerns in neutrosophic normed spaces, our approach facilitates enhanced understanding and control of complex systems characterized by indeterminacy and uncertainty. The primary focus of this research is to propose a novel class of Euler-Lagrange additive FE and investigate its Ulam-Hyers stability in neutrosophic normed spaces. Direct and fixed point techniques are utilized to achieve the required results.
The Banach fixed point theorem and the nonlinear alternative of Leray–Schauder type are used to investigate the existence of solutions for fractional order functional and neutral functional ...differential equations with infinite delay.
The standard twist
$F(s,\unicodeSTIX{x1D6FC})$
of
$L$
-functions
$F(s)$
in the Selberg class has several interesting properties and plays a central role in the Selberg class theory. It is therefore ...natural to study its finer analytic properties, for example the functional equation. Here we deal with a special case, where
$F(s)$
satisfies a functional equation with the same
$\unicodeSTIX{x1D6E4}$
-factor of the
$L$
-functions associated with the cusp forms of half-integral weight; for simplicity we present our results directly for such
$L$
-functions. We show that the standard twist
$F(s,\unicodeSTIX{x1D6FC})$
satisfies a functional equation reflecting
$s$
to
$1-s$
, whose shape is not far from a Riemann-type functional equation of degree 2 and may be regarded as a degree 2 analog of the Hurwitz–Lerch functional equation. We also deduce some results on the growth on vertical strips and on the distribution of zeros of
$F(s,\unicodeSTIX{x1D6FC})$
.
In this paper, we introduce a new quadratic functional equation and, motivated by this equation, we investigate
n
-variables mappings which are quadratic in each variable. We show that such mappings ...can be unified as an equation, namely, multi-quadratic functional equation. We also apply a fixed point technique to study the stability for the multi-quadratic functional equations. Furthermore, we present an example and a few corollaries corresponding to the stability and hyperstability outcomes.
In this paper, we introduce the functional equations
f
(
2
x
−
y
)
+
f
(
x
+
2
y
)
=
5
f
(
x
)
+
f
(
y
)
,
f
(
2
x
−
y
)
+
f
(
x
+
2
y
)
=
5
f
(
x
)
+
4
f
(
y
)
+
f
(
−
y
)
,
f
(
2
x
−
y
)
+
f
(
x
...+
2
y
)
=
5
f
(
x
)
+
f
(
2
y
)
+
f
(
−
y
)
,
f
(
2
x
−
y
)
+
f
(
x
+
2
y
)
=
4
f
(
x
)
+
f
(
y
)
+
f
(
−
x
)
+
f
(
−
y
)
.
We show that these functional equations are quadratic and apply them to characterization of inner product spaces. We also investigate the stability problem on restricted domains. These results are applied to study the asymptotic behaviors of these quadratic functions in complete
β
-normed spaces.
In an integrated and self-contained fashion, this book covers almost all classical results on the Hyers-Ulam-Rassias stability. It is arranged so that highly advanced undergraduate as well as ...graduate level students will be able to follow the materials.
In this article, a new class of real-valued Euler–Lagrange symmetry additive functional equations is introduced. The solution of the equation is provided, assuming the unknown function to be ...continuous and without any regularity conditions. The objective of this research is to derive the Hyers–Ulam–Rassias stability (HURS) in intuitionistic fuzzy normed spaces (IFNS) by applying the classical direct method and fixed point techniques (FPT). Furthermore, it is proven that the Euler–Lagrange symmetry additive functional equation and the control function, which is the IFNS of the sums and products of powers of norms, is stable. In addition, a few examples where the solution of this equation can be applied in Fourier series and Fourier transforms are demonstrated.
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