The results presented in this paper deal with the classical but still prevalent problem of introducing new classes of m-fold symmetric bi-univalent functions and studying properties related to ...coefficient estimates. Quantum calculus aspects are also considered in this study in order to enhance its novelty and to obtain more interesting results. We present three new classes of bi-univalent functions, generalizing certain previously studied classes. The relation between the known results and the new ones presented here is highlighted. Estimates on the Taylor–Maclaurin coefficients |am+1| and |a2m+1| are obtained and, furthermore, the much investigated aspect of Fekete–Szegő functional is also considered for each of the new classes.
In this paper, we introduce three new subclasses of m-fold symmetric holomorphic functions in the open unit disk U, where the functions f and f−1 are m-fold symmetric holomorphic functions in the ...open unit disk. We denote these classes of functions by FSΣ,mp,q,s(d), FSΣ,mp,q,s(e) and FSΣ,mp,q,s,h,r. As the Fekete-Szegö problem for different classes of functions is a topic of great interest, we study the Fekete-Szegö functional and we obtain estimates on coefficients for the new function classes.
In our present investigation, we introduce and study some new subclasses of analytic functions associated with Ruscheweyh differential operator Dr. We obtain a Fekete–Szegö inequality for certain ...normalized analytic function defined on the open unit disk for which Drl′(z)ϑzDrl′(z)Drl(z)1−ϑ≺ez (0≤ϑ≤1) lies in a starlike region with respect to 1 and symmetric with respect to the real axis. As a special case of this result, the Fekete–Szegö inequality for a class of functions defined through Poisson distribution series is obtained.
For k-Riemann–Liouville fractional integral operators, the Hermite–Hadamard inequality is already well-known in the literature. In this regard, this paper presents the Hermite–Hadamard inequalities ...for k-Riemann–Liouville fractional integral operators by using a novel method based on Green’s function. Additionally, applying these identities to the convex and monotone functions, new Hermite–Hadamard type inequalities are established. Furthermore, a different form of the Hermite–Hadamard inequality is also obtained by using this novel approach. In conclusion, we believe that the approach presented in this paper will inspire more research in this area.
The objective of this paper is to introduce new classes of m-fold symmetric bi-univalent functions. We discuss estimates on the Taylor–Maclaurin coefficients
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a
m
+
1
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and
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a
2
m
+
1
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, and the ...Fekete–Szegő problem is also considered for the new classes of functions introduced. We denote these classes by
M
F
−
S
Σ
,
m
p
,
q
(
h
)
,
M
F
−
S
Σ
,
m
p
,
q
(
s
)
, and
M
F
−
S
Σ
,
m
b
,
d
. Quantum calculus aspects are also considered in this study to enhance its novelty and to obtain more interesting results.
The object of this article is to explore a τ-pseudo-ν-convex κ-fold symmetric bi-univalent function family satisfying subordinations condition generalizing certain previously examined families. We ...originate the initial Taylor–Maclaurin coefficient estimates of functions in the defined family. The classical Fekete–Szegö inequalities for functions in the defined τ-pseudo-ν-convex family is also estimated. Furthermore, we present some of the special cases of the main results. Relevant connections with those in several earlier works are also pointed out. Our study in this paper is also motivated by the symmetry nature of κ-fold symmetric bi-univalent functions in the defined class.
In this paper, we introduce and investigate two new subclasses of analytic and bi-univalent functions using the q-derivative operator Dq0<q<1 and the Gegenbauer polynomials in a symmetric domain, ...which is the open unit disc Λ=℘:℘∈Cand℘<1. For these subclasses of analytic and bi-univalent functions, the coefficient estimates and Fekete–Szegö inequalities are solved. Some special cases of the main results are also linked to those in several previous studies. The symmetric nature of quantum calculus itself motivates our investigation of the applications of such quantum (or q-) extensions in this paper.
We consider three new classes of meromorphic functions defined by an extension of the Wanas operator and two integral operators, in order to study some preservation properties of the classes. The ...purpose of the paper is to find the conditions such that, when we apply the integral operator Jp,γ to some function from the new defined classes ΣSp,qn(α,δ), respectively ΣSp,qn(α), we obtain also a function from the same class. We also define a new integral operator on the class of meromorphic functions, denoted by Jp,γ,h, where h is a normalized analytic function on the unit disc. We study some basic properties of this operator. Then we look for the conditions which allow this operator to preserve a particular subclass of the classes mentioned above.
In the current article, making use of certain operator, we initiate and explore a certain family WΣ(λ,γ,σ,δ,α,β,p,q;h) of holomorphic and bi-univalent functions in the open unit disk D. We establish ...upper bounds for the initial Taylor–Maclaurin coefficients and the Fekete–Szegö type inequality for functions in this family.
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