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In this paper, we employ a q -Noor integral operator to perform a q -analogue of certain fractional integral operator defined on an open unit disc. Then, we make use of the Hadamard convolution product to discuss several related results. Also, we derive a class of convex functions by utilizing the q -fractional integral operator and apply the inspired presented theory of the differential subordination, to geometrically explore the most popular differential subordination properties of the aforementioned operator. In addition, we discuss an exciting inclusion for the given convex class of functions. Over and above, we investigate the q -fractional integral operator and obtain some applications for the differential subordination. [ABSTRACT FROM AUTHOR]

In this paper, we give a characterization of Fredholmness of the Toeplitz operators on the Bergman spaces A φ p with exponential weights in D when 0 < p < ∞. Also, we obtain the sufficient and necessary conditions which the Toeplitz and Hankel operators on A φ 2 belong to h -Schatten class, where h is a continuous increasing convex function. [ABSTRACT FROM AUTHOR]

The study of convex functions is an interesting area of research due to its huge applications in pure and applied mathematics special in optimization theory. The aim of this paper is to introduce and study a more generalized class of convex functions. We established Schur (S), Hermite-Hadamard (HH), and Fejér (F) type inequalities for introduced class of convex functions. The results presented in this paper extend and generalize many existing results of the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study a generalized version of strongly reciprocally convex functions of higher order. Firstly, we prove some basic properties for addition, scalar multiplication, and composition of functions. Secondly, we establish Hermite-Hadamard and Fejér type inequalities for the generalized version of strongly reciprocally convex functions of higher order. We also include some fractional integral inequalities concerning with this class of functions. Our results have applications in optimization theory and can be considered extension/generalization of many existing results. [ABSTRACT FROM AUTHOR]

The fractional integral inequalities are crucial to deal applied problems. The present paper deals with the generalize midpoint type inequalities for a certain class of convex functions, namely, MT-convex functions in the setting of weighted fractional integral. It can be observed from the remarks given in the paper that our results or more generalized than existing results of literature and many of them can be obtained immediately from our results. [ABSTRACT FROM AUTHOR]

This paper derives some equalities via twice differentiable functions and conformable fractional integrals. With the help of the obtained identities, we present new trapezoid-type and midpoint-type inequalities via convex functions in the context of the conformable fractional integrals. New inequalities are obtained by taking advantage of the convexity property, power mean inequality, and Hölder's inequality. We show that this new family of inequalities generalizes some previous research studies by special choices. Furthermore, new other relevant results with trapezoid-type and midpoint-type inequalities are obtained. [ABSTRACT FROM AUTHOR]

In 2003, Mercer presented an interesting variation of Jensen's inequality called Jensen–Mercer inequality for convex function. In the present paper, by employing harmonically convex function, we introduce analogous versions of Hermite–Hadamard inequalities of the Jensen–Mercer type via fractional integrals. As a result, we introduce several related fractional inequalities connected with the right and left differences of obtained new inequalities for differentiable harmonically convex mappings. As an application viewpoint, new estimates regarding hypergeometric functions and special means of real numbers are exemplified to determine the pertinence and validity of the suggested scheme. Our results presented here provide extensions of others given in the literature. The results proved in this paper may stimulate further research in this fascinating area. [ABSTRACT FROM AUTHOR]

In the present paper, q -fractional integral operators are used to construct quantum analogue of Ostrowski type inequalities for the class of s -convex functions. The limiting cases include the nonfractional existing cases from literature. Specially, Ostrowski type inequalities for q -integrals and Ostrowski type inequalities for convex functions are deduced. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new Newton's type inequalities for differentiable convex functions using the generalized Riemann-Liouville fractional integrals. The main edge of the newly established inequalities is that these can be turned into several new and existing inequalities for different fractional integrals like Riemann-Liouville fractional integrals, k -fractional integrals, Katugampola fractional operators, conformable fractional operators, Hadamard fractional operators, and fractional operators with the exponential kernel without proving one by one. It is also shown that the newly established inequalities are the refinements of the previously established inequalities inside the literature. [ABSTRACT FROM AUTHOR]

In the present paper, we deal with some fractional integral inequalities for strongly reciprocally p , h -convex functions. We established fractional version of Hermite-Hadamard and Fejér type inequalities for strongly reciprocally p , h -convex functions. Our results extend and generalize many exiting results of literate. [ABSTRACT FROM AUTHOR]

In this paper, we concern with the split feasibility problem (SFP) whenever the convex sets involved are composed of level sets. By applying Gradient-projection algorithm which is used to solve constrained convex minimization problem of a real valued convex function, we construct two new algorithms for the split feasibility problem and prove that both of them are convergent weakly to a solution of the feasibility problem. In the end, as an application, we obtain a new algorithm for solving the split equality problem. [ABSTRACT FROM AUTHOR]

The new outcomes of the present paper are q -analogues (q stands for quantum calculus) of Hermite-Hadamard type inequality, Montgomery identity, and Ostrowski type inequalities for s -convex mappings. Some new bounds of Ostrowski type functionals are obtained by using Hölder, Minkowski, and power mean inequalities via quantum calculus. Special cases of new results include existing results from the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of uniform harmonic χ -convex functions. We show that this class relates several other unrelated classes of uniform harmonic convex functions. We derive a new version of Hermite-Hadamard's inequality and its fractional analogue. We also derive a new fractional integral identity using Caputo-Fabrizio fractional integrals. Utilizing this integral identity as an auxiliary result, we obtain new fractional Dragomir-Agarwal type of inequalities involving differentiable uniform harmonic χ -convex functions. We discuss numerous new special cases which show that our results are quite unifying. Finally, in order to show the significance of the main results, we discuss some applications to means of positive real numbers. [ABSTRACT FROM AUTHOR]

In this study, the modification of the concept of exponentially convex function, which is a general version of convex functions, given on the coordinates, is recalled. With the help of an integral identity which includes the Riemann-Liouville (RL) fractional integral operator, new Hadamard-type inequalities are proved for exponentially convex functions on the coordinates. Many special cases of the results are discussed. [ABSTRACT FROM AUTHOR]

In this particular research article, we take an analytic function Q 4 L = 1 + 5 / 6 z + 1 / 6 z 5 , which makes a four-leaf-shaped image domain. Using this specific function, two subclasses, S 4 L ∗ and C 4 L , of starlike and convex functions will be defined. For these classes, our aim is to find some sharp bounds of inequalities that consist of logarithmic coefficients. Among the inequalities to be studied here are Zalcman inequalities, the Fekete-Szegö inequality, and the second-order Hankel determinant. [ABSTRACT FROM AUTHOR]

In this study, a new Simpson type conformable fractional integral equality for convex functions is established. Based on this identity, some results related to Simpson-like type inequalities are obtained. Also, some estimation results are given for the special cases of the derivative of a function used in our results, and some applications are presented for special means such as the arithmetic, geometric, and logarithmic means. [ABSTRACT FROM AUTHOR]

In this article, we consider the class of modified h − convex functions and derive the famous Giaccardi and Petrovi c ′ type inequalities for this class of functions. The mean value theorems for the functionals due to Giaccardi and Petrovi c ′ type inequalities are formulated. Some special cases are discussed by taking different examples of function h. [ABSTRACT FROM AUTHOR]

The main objective of this article is to establish generalized fractional Hermite–Hadamard and related type integral inequalities for h -Godunova–Levin convexity and h -Godunova–Levin preinvexity with extended Wright generalized Bessel function acting as kernel. Moreover, Hermite–Hadamard-type and trapezoid-type inequalities for several known convexities including Godunova–Levin function, classical convex, s -Godunova–Levin function, P -function, and s -convex function are deduced as corollaries. These obtained results are analyzed in the form of generalization of fractional inequalities. [ABSTRACT FROM AUTHOR]

The intention of this note is to investigate some new important estimates for the Jensen gap while utilizing a 4-convex function. We use the Jensen inequality and definition of convex function in order to achieve the required estimates for the Jensen gap. We acquire new improvements of the Hölder and Hermite–Hadamard inequalities with the help of the main results. We discuss some interesting relations for quasi-arithmetic and power means as consequences of main results. At last, we give the applications of our main inequalities in the information theory. The approach and techniques used in the present note may simulate more research in this field. [ABSTRACT FROM AUTHOR]

Due to applications in almost every area of mathematics, the theory of convex and nonconvex functions becomes a hot area of research for many mathematicians. In the present research, we generalize the Hermite–Hadamard-type inequalities for p , h -convex functions. Moreover, we establish some new inequalities via the Caputo-Fabrizio fractional integral operator for p , h -convex functions. Finally, the applications of our main findings are also given. [ABSTRACT FROM AUTHOR]

In the present research, we generalize the midpoint inequalities for strongly convex functions in weighted fractional integral settings. Our results generalize many existing results and can be considered as extension of existing results. [ABSTRACT FROM AUTHOR]

The aim of this particular article is at studying a holomorphic function f defined on the open-unit disc D = z ∈ ℂ : z < 1 for which the below subordination relation holds z f ′ z / f z ≺ q 0 z = 1 + tan h z. The class of such functions is denoted by S tan h ∗. The radius constants of such functions are estimated to conform to the classes of starlike and convex functions of order β and Janowski starlike functions, as well as the classes of starlike functions associated with some familiar functions. [ABSTRACT FROM AUTHOR]

Recently, many fractional integral operators were introduced by different mathematicians. One of these fractional operators, Atangana-Baleanu fractional integral operator, was defined by Atangana and Baleanu (Atangana and Baleanu, 2016). In this study, firstly, a new identity by using Atangana-Baleanu fractional integral operators is proved. Then, new fractional integral inequalities have been obtained for convex and concave functions with the help of this identity and some certain integral inequalities. [ABSTRACT FROM AUTHOR]