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In this note, we slightly generalize Theorem 2 in the paper by M. Tunç and point out that the assumption of Theorem 3 is not sufficient. A misuse of the term 'mean' is also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we give an equality for the case of differentiable convex functions involving conformable fractional integrals. Bullen-type inequalities for the conformable fractional integrals are established by using this equality. Some important inequalities are obtained by taking advantage of the convexity, the Hölder inequality and the power mean inequality. By using special choices, we present some known results in the literature. Furthermore, we give an example using a graph in order to show that our main results are correct. [ABSTRACT FROM AUTHOR]

In this paper, we prove an identity for differentiable convex functions related to conformable fractional integrals. Moreover, some parameterized inequalities are established by using conformable fractional integrals. To be more precise, parameterized inequalities are obtained by taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Furthermore, previous and new results are presented by using special cases of the obtained theorems. [ABSTRACT FROM AUTHOR]

This paper establishes an identity for the case of differentiable s-convex functions with respect to the conformable fractional integrals. By using this identity, sundry trapezoid-type inequalities are proven by s-convex functions with the help of the conformable fractional integrals. Several important inequalities are acquired with taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Moreover, an example using graph is given in order to show that our main results are correct. By using the special choices of the obtained results, we present several new results connected with trapezoid-type inequalities. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and examine certain subclass Mq,Σ (φ, β) of analytic and bi-univalent functions on the open unit disk in the complex plane. Here, we give coefficient bound estimates, upper bound estimate for the second Hankel determinant and Fekete-Szegö inequality for the function belonging to this class. Some interesting special cases of the results obtained here are also discussed. [ABSTRACT FROM AUTHOR]

Let Jv(z) denote the Bessel function of the first kind of order v. In this paper, our aim is to determine the radii of starlikeness and convexity for three kind of normalization of the function Nv(z) = az²Jv"(z) + bzvJ' (z) + cJv(z) in the case where zeros are all real except for a single pair, which are conjugate purely imaginary. The key tools in the proof of our main results are the Mittag--Leffler expansion for function Nv(z) and properties of real and complex zeros of it. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to investigate the starlikeness, convexity, and close-to-convexity of some partial sums of the generalized Koebe function. Furthermore, we give some special results related with special cases of c constant. The results, which are presented in this paper, would generalize those in related works of several earlier authors. [ABSTRACT FROM AUTHOR]

Let T be the class of analytic functions in the open unit disc U with f(0) = 0 and f ′ (0) = 1. For f(z) ∈ T, the Alexander integral operator A-1f(z), the Libera integral operator L-1f(z) and the Bernardi integral operator B-1f(z) were considered before. Using A-1f(z) and L-1f(z), a new integral operator Fλf(z) is considered. After discuss some properties of dominant for Fλf(z), another new integral operator O-1f(z) of f(z) ∈ T is discussed. The object of the present paper is to discuss the dominant of new integral operators Fλf(z) and O-1f(z) concerning with some starlike functions and convex functions in U. [ABSTRACT FROM AUTHOR]

The main objective of the present paper is to give with using the linear operator theory and also hypergeometric representations of related functions a new special subclass T Sp(2-r, 2-1), r ∈ Z+ of uniformly convex functions and in addition a suitable subclass of starlike functions with negative Taylor coefficients. Furthermore, the provided trailblazer outcomes in presented study are generalized to certain functions classes with fixed finitely many Taylor coefficients. [ABSTRACT FROM AUTHOR]

In this paper, we obtain an important inequalities for coordinated convex functions and as a result of these inequalities we give the extension of Hermite–Hadamard type inequalities for Riemann–Liouville fractional integral and logarithmic integral. The inequalities obtained in this study provide generalizations of some result given in earlier works. [ABSTRACT FROM AUTHOR]

In this paper, we study singular integrals along compound curves with Hardy space kernels. We introduce a class of bidirectional generalized Hardy Littlewood maximal functions. We prove that the considered singular integrals and the maximal functions are bounded on Lp, 1 < p < ∞ provided that the compound curves are determined by generalized polynomials and convex increasing functions. The obtained results offer Lp estimates that are not only new but also they generalize as well as improve previously known results. [ABSTRACT FROM AUTHOR]

In this paper we consider two subclasses B(p, q, α, β) and B1(p, q, α, β) of p-valently Bazilević functions defined by higher order derivatives, and we defined and studied some properties of the images of the functions of these classes by the integral operators In,p and Jn,p for multivalent functions, defined by using higher order derivatives. [ABSTRACT FROM AUTHOR]

In this paper we deal with the radii of starlikeness and convexity of the q -Mittag-Leffler function for three different kinds of normalization by making use of their Hadamard factorization in such a way that the resulting functions are analytic in the unit disk of the complex plane. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-Pólya class of real entire functions plays a pivotal role in this investigation. [ABSTRACT FROM AUTHOR]

In recent years, applications of Bessel differential equations have been commonly used in univalent functions theory. The main object of the present paper is to give some characteristic properties for some subclasses of uniformly starlike and convex functions which are defined here by means of the normalized form of the generalized Bessel function to be univalent in the open unit disc. Furthermore, we also establish some results of these subclasses related to a particular integral operator. Some corresponding consequences of our main results are also considered. [ABSTRACT FROM AUTHOR]

Recently, in the literature, we can see quite a few papers about general coefficient bounds for subclasses of bi-univalent functions. However, we can find just a few papers about general coefficient estimates for subclasses of bi-close-to-convex functions. In the present study, we give and look into a new subclass of analytic and bi-close-to-convex functions in the open unit disk. Making use of the Faber series, we have an upper bound for the general coefficient of functions in this class. We also demonstrate the invisible behavior of the beginning coefficients of a special subclass of bi-close-to-convex functions. [ABSTRACT FROM AUTHOR]

In a very recent work, Şeker and Sümer Eker [On subclasses of bi-close-to-convex functions related to the odd-starlike functions. Palestine Journal of Mathematics 2017; 6: 215-221] defined two subclasses of analytic bi-closeto- convex functions related to the odd-starlike functions in the open unit disk U. The main purpose of this paper is to generalize and improve the results of Şeker and Sümer Eker (in the aforementioned study) defining a comprehensive subclass of bi-close-to-convex functions. Also, we investigate the Fekete-Szegö type coefficient bounds for functions belonging to this new class. [ABSTRACT FROM AUTHOR]

In this paper we derive some properties of multivalent functions belonging to the classes Rp,q(α), Bp,q(α), and Mp,q(α) . The results obtained generalize the related works of some authors, and many other new results are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate an analytic function class Pq( λ, A, B) that we call the class of q-starlike and q-convex functions with respect to the parameter λ. We give coefficient bounds estimates, distortion bound and growth theorems for the functions belonging to this class. [ABSTRACT FROM AUTHOR]

Let (βn)n≥2 be a sequence of nonnegative real numbers and δ be a positive real number. We introduce the subclass A(βn, δ) of analytic functions, with the property that the Taylor coefficients of the function f satisfies Σ∞n≥2βn︱an︱≤ δ, where f(z) = z + Σ∞n=2 anzn . The class A(βn, δ) contains nonunivalent functions for some choices of (βn)n≥2 . In this paper, we provide some general properties of functions belonging to the class A(βn, δ), such as the radii of univalence, distortion theorem, and invariant property. Furthermore, we derive the best approximation of an analytic function in such class by using the semiinfinite quadratic programming. Applying our results, we recover some known results on subclasses related to coefficient inequality. Some applications to starlike and convex functions of order α are also mentioned. [ABSTRACT FROM AUTHOR]

Let SH be the class of functions f = h + ḡ that are harmonic univalent and sense-preserving in the open unit disk 핌 = {z ∈ ℂ : |z| < 1}, where h, g are analytic and fz' (0) = fZ(0) - 1 = 0 in 핌. In this paper, we investigate the properties of some subclasses of SH such that h(z) is a starlike (or convex) function defined by subordination. We provide coefficient estimates, extremal function, distortion and growth estimates of g, growth, and Jacobian estimates of f. We also obtain area estimates and covering theorems of the classes. The results presented here generalize some known results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of estimating |a4 -a2a3|, where ak are the coefficients of a given close-to-convex function. The bounds of this expression for various classes of analytic functions have been applied to estimate the third Hankel determinant H3(1) . The results for two subclasses of the class C of all close-to-convex functions are sharp. This bound is equal to 2. It is conjectured that this number is also the exact bound of |a4 -a2a3| for the whole class C. [ABSTRACT FROM AUTHOR]

In the paper we discuss two functionals of the Fekete-Szegö type: Φf(µ) = a2a4 -- µ,a3² and ©/(µ) = a4 -- µa2a3 for an analytic function f (z) = z + a2z² + a3z³ + . . ., z € Δ, (Δ = {z € C : |z| < 1}) and a real number µ. We focus our research on the estimation of (µ)| and \©f (µ)|, while f is either in S* (the class of starlike functions) or in Κ (the class of convex functions). [ABSTRACT FROM AUTHOR]

In this paper we consider some normalized Bessel, Struve, and Lommel functions of the first kind and, by using the Euler{Rayleigh inequalities for the first positive zeros of a combination of special functions, we obtain tight lower and upper bounds for the radii of starlikeness of these functions. By considering two different normalizations of Bessel and Struve functions we give some inequalities for the radii of convexity of the same functions. On the other hand, we show that the radii of univalence of some normalized Struve and Lommel functions are exactly the radii of starlikeness of the same functions. In addition, by using some ideas of Ismail and Muldoon we present some new lower and upper bounds for the zeros of derivatives of some normalized Struve and Lommel functions. The Laguerre-Pólya class of real entire functions plays an important role in our study. [ABSTRACT FROM AUTHOR]

In this paper we derive several improved forms of the Jensen inequality, giving the necessary and sufficient conditions for them to hold in the case of the real Stieltjes measure not necessarily positive. The obtained relations are characterized via the Green function. As an application, our main results are employed for constructing some classes of exponentially convex functions and some Cauchy-type means. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class Kαof all functions f univalent in the unit disk Δ that are normalized by f(0) = f' (0) - 1 = 0 while the sets f(Δ) are convex in two symmetric directions: eiαπ/2 and e -iαπ/2, α ∈ [0, 1] . It means that the intersection of f(Δ) with each straight line having the direction eiαπ/2 or e-iαπ/2 is either a compact set or an empty set. We find the Koebe set for Kα. Moreover, we perform the same operation for functions in Kβ,γ, i.e. for functions that are convex in two fixed directions: eiβπ/2 and eiγπ/2, -1 ≤ β ≤ γ γ ≤ 1. [ABSTRACT FROM AUTHOR]

In this paper, we establish some generalized Ostrowski-type inequalities for functions whose first derivatives absolute values are convex. [ABSTRACT FROM AUTHOR]

In this paper we introduce the class of m-valent Janowski close to convex harmonic functions. Growth and distortion theorems are obtained for this class. Our study is based on the harmonic shear methods for harmonic functions. [ABSTRACT FROM AUTHOR]

In the present paper we establish some new integral inequalities analogous to the well known Hadamard's inequality by using a fairly elementary analysis. [ABSTRACT FROM AUTHOR]

Let Ap denote the class of functions of the form f (z) = zp+ap+1 zp+1+a p+2zp+2+…which are regular and p-valent in the open unit disc D = {z : |z| < 1}. Let Mp(α) be the subclass of Ap consisting of functions f(z) which satisfy Re (z f′ (z)/ f(z) < α, (z ε D) for some real α (α > 1). The aim of this paper is to give a representation theorem, a distortion theorem and a coefficient inequality for the class Mp(α). [ABSTRACT FROM AUTHOR]