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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]

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]