Abstract
In this current work, we examine the Hyers-Ulam(H-U) stability results for a finite variable additive functional equation (Ref.6) in Intuitionistic Fuzzy Normed space(IFN-space) is discussed ...by means of direct and fixed point methods.
The functional equation of associativity is the topic of Abel's first contribution to Crelle's Journal. Seventy years later, it was featured as the second part of Hilbert's Fifth Problem, and it was ...solved under successively weaker hypotheses by Brouwer (1909), Cartan (1930) and Aczel (1949). In 1958, B Schweizer and A Sklar showed that the “triangular norms” introduced by Menger in his definition of a probabilistic metric space should be associative; and in their book Probabilistic Metric Spaces, they presented the basic properties of such triangular norms and the closely related copulas. Since then, the study of these two classes of functions has been evolving at an ever-increasing pace and the results have been applied in fields such as statistics, information theory, fuzzy set theory, multi-valued and quantum logic, hydrology, and economics, in particular, risk analysis. This book presents the foundations of the subject of associative functions on real intervals. It brings together results that have been widely scattered in the literature and adds much new material. In the process, virtually all the standard techniques for solving functional equations in one and several variables come into play. Thus, the book can serve as an advanced undergraduate or graduate text on functional equations.
In this paper we provide a characterization theorem for set-valued solutions of the functional equation
for the case of compact, convex valued maps. We prove that every solution of the functional ...equation is the sum of an additive single-valued function and a nonempty compact and convex set.
Feynman integrals obey linear relations governed by intersection numbers, which act as scalar products between vector spaces. We present a general algorithm for the construction of multivariate ...intersection numbers relevant to Feynman integrals, and show for the first time how they can be used to solve the problem of integral reduction to a basis of master integrals by projections, and to directly derive functional equations fulfilled by the latter. We apply it to the decomposition of a few Feynman integrals at one and two loops, as first steps toward potential applications to generic multiloop integrals. The proposed method can be more generally employed for the derivation of contiguity relations for special functions admitting multifold integral representations.
In this paper, a computer program developed in the computer algebra system Maple is presented, which investigates alienness and strong alienness of linear functional equations.
ON THE PELL-EISENSTEIN SERIES OF POWER m Inam, Ilker; Özkan, Engin; Özkaya, Zeynep Demirkol ...
Bulletin of the Transilvania University of Brașov. Series III, Mathematics, informatics, physics,
01/2022, Letnik:
2, Številka:
1
Journal Article
In this paper, we introduce the Pell-Eisenstein Series which are obtained by Pell numbers and they are a new class of Eisenstein-type series. First we see that they are well-defined and then we prove ...that the Pell-Eisenstein series satisfies some functional equations. Proofs are based on properties of Pell numbers and calculations.
We extend results of Knopp in 9 to the higher level case. In precise, we characterize a rational period function q(z) for Г+(2) of which poles lie only in Q U {u}. We prove that the Mellin transform ...Ф_р (s) of an entire modular integral F of weight 2k for such a rational period function q(z) has an analytic continuation to the entire s-plane, except for possible simple poles at some rational integers, satisfies the functional equation Ф_^(2k - s) = (-1)k2s~?F(s), and is bounded on each "truncated strip" of the from u\ < Re(s) < a2 and |Im(s)| > t0 > 0. We also show that the converse is true. The case for Г+(3) is addressed similarly.
In this paper we present some methods for solving a large class of composite functional equations. These methods are then applied to the functional equations
1
f
(
a
f
(
x
)
f
(
y
)
+
b
(
f
(
x
)
y
+
...f
(
y
)
x
)
+
c
x
y
)
=
f
(
x
)
f
(
y
)
2
f
(
a
f
(
x
)
k
y
+
b
f
(
y
)
ℓ
x
+
c
x
y
)
=
f
(
x
)
f
(
y
)
with
a
,
b
,
c
∈
R
and
k
,
ℓ
∈
N
∪
{
0
}
, for which we obtain all continuous solutions
f
:
R
→
R
. These equations generalize some well-known composite functional equations.
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