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In this paper, we first prove three identities for twice partially differentiable functions. Then, by using these equalities, we obtain several trapezoid and Ostrowski type inequalities via generalized fractional integrals for functions with bounded partial derivatives. Moreover, we present some results for Riemann-Liouville fractional integrals by special choice of main results. WOS:000687664600001 2-s2.0-85113769051

In this paper, we obtain some Hermite-Hadamard type inequalities for h-convex functions. Also, some applications to special means of real numbers are given. The results presented here provide extensions of those given in earlier works. WOS:000537926700002 2-s2.0-85086095154

In this article, we use quantum integrals to derive Hermite–Hadamard inequalities for preinvex functions and demonstrate their validity with mathematical examples. We use the qϰ2-quantum integral to show midpoint and trapezoidal inequalities for qϰ2-differentiable preinvex functions. Furthermore, we demonstrate with an example that the previously proved Hermite–Hadamard-type inequality for preinvex functions via qϰ1-quantum integral is not valid for preinvex functions, and we present its proper form. We use qϰ1-quantum integrals to show midpoint inequalities for qϰ1-differentiable preinvex functions. It is also demonstrated that by considering the limit q→1− and ηϰ2,ϰ1=−ηϰ1,ϰ2=ϰ2−ϰ1 in the newly derived results, the newly proved findings can be turned into certain known results.

In this investigation, for convex functions, some new (p,q)–Hermite–Hadamard-type inequalities using the notions of (p,q)π2 derivative and (p,q)π2 integral are obtained. Furthermore, for (p,q)π2-differentiable convex functions, some new (p,q) estimates for midpoint and trapezoidal-type inequalities using the notions of (p,q)π2 integral are offered. It is also shown that the newly proved results for p=1 and q→1− can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities.

In this work, we establish inequalities of Hermite-Hadamard-Mercer (HHM) type for convex functions by using generalized fractional integrals. The results of our paper are the extensions and refinements of Hermite-Hadamard (HH) and Hermite-Hadamard-Mercer (HHM) type inequalities. We discuss special cases of our main results and give new inequalities of HH and HHM type for different fractional integrals like, Riemann-Liouville (RL) fractional integrals, k-Riemann-Liouville (k-RL) fractional integrals, conformable fractional integrals and fractional integrals of exponential kernel. National Natural Sciences Foundation of ChinaNational Natural Science Foundation of China (NSFC) [11971241] We want to give thanks to the Direccion de investigacion from Pontificia Universidad Catolica del Ecuador for technical support to our research project entitled: Algunas desigualdades integrales para funciones convexas generalizadas y aplicaciones. This work is partially supported by National Natural Sciences Foundation of China (Grant No. 11971241) . WOS:000685892800017 2-s2.0-85108365098

In this work, firstly, we obtain a new identity with some parameters for generalized fractional integrals. Then by utilizing this obtained equality, we establish some new parameterized inequalities for coordinated convex functions via generalized fractional integrals. In addition, in a separate section, we show that the results given in the main section reduce to several trapezoid, midpoint, and Simpson type inequalities for various values of parameters. WOS:000664125700001 2-s2.0-85108265701

In this study, we prove an identity for twice partially differentiable mappings involving the double generalized fractional integral and some parameters. By using this established identity, we offer some generalized inequalities for differentiable co-ordinated convex functions with a rectangle in the plane $\mathbb{R} ^{2}$ R 2 . Furthermore, by special choice of parameters in our main results, we obtain several well-known inequalities such as the Ostrowski inequality, trapezoidal inequality, and the Simpson inequality for Riemann and Riemann–Liouville fractional integrals.

Integral inequality plays a critical role in both theoretical and applied mathematics fields. It is clear that inequalities aim to develop different mathematical methods (numerically or analytically) and to dedicate the convergence and stability of the methods. Unfortunately, mathematical methods are useless if the method is not convergent or stable. Thus, there is a present day need for accurate inequalities in proving the existence and uniqueness of the mathematical methods. Convexity play a concrete role in the field of inequalities due to the behaviour of its definition. There is a strong relationship between convexity and symmetry. Which ever one we work on, we can apply to the other one due to the strong correlation produced between them especially in recent few years. In this article, we first introduced the notion of &lambda, incomplete gamma function. Using the new notation, we established a few inequalities of the Hermite&ndash, Hadamard (HH) type involved the tempered fractional integrals for the convex functions which cover the previously published result such as Riemann integrals, Riemann&ndash, Liouville fractional integrals. Finally, three example are presented to demonstrate the application of our obtained inequalities on modified Bessel functions and q-digamma function.

In this paper, we first give a lemma for twice differentiable function to obtain trapezoid and midpoint inequalities. By using this lemma, we establish some inequalities for mapping whose second derivatives in absolute value are convex via Riemann-Liouville fractional integrals. These results generalize the midpoint and trapezoid inequalities involving Riemann-Liouville fractional integrals given in earlier studies. WOS:000610186900007

In this paper we obtain new generalization of Hermite-Hadamard inequalities via generalized fractional integrals defined by Sarikaya and Ertugral. We establish some midpoint and trapezoid type inequalities for functions whose first derivatives in absolute value are convex involving generalized fractional integrals. WOS:000677398600014 2-s2.0-85102836811

The purpose of this paper is to establish some Hermite-Hadamard type inequalities for h-convex functions utilizing generalized fractional integrals. We also obtain some generalized trapezoid and midpoint type inequalities for the mapping whose first derivatives absolutely value are h-convex. The results proved in this paper generalize the several inequalities obtained earlier works National Natural Science Foundation of ChinaNational Natural Science Foundation of China (NSFC) [11971241] This project is partially supported by the National Natural Science Foundation of China(No. 11971241). WOS:000659073000011

Our first aim is to establish two new identities for differentiable function involving Riemann-Liouville fractional integrals. Then, we obtain some new weighted versions of fractional trapezoid and Ostrowski type inequalities. Moreover, we give some weighted fractional midpoint type inequalities as special cases. WOS:000520850800021 2-s2.0-85079871798

In this paper, we present a new definition which generalizes some significant well known fractional integral operators such as Riemann-Liouville fractional integral, k-Riemann-Liouville fractional integral, Katugampola fractional operators, conformable fractional integral, Hadamard fractional integrals, etc. Then, using a general class of this generalized fractional integral operator, we establish new generalized fractional integral inequalities of Hermite-Hadamard type which cover the previously published results. WOS:000557032900016 2-s2.0-85091852295

Selected papers of International Conference on Life and Engineering Sciences (ICOLES 2018), Kyrenia, Cyprus, 2-6 September, 2018. In this paper, we establish new refinements and integral inequalities including concave functions. The reason why we choose the concave functions in this study is that the methods we use are applicable to these functions. Also some applications are provided. Publisher's Version

Selected papers of International Conference on Life and Engineering Sciences (ICOLES 2018), Kyrenia, Cyprus, 2-6 September, 2018. In this paper, we establish a few new generalization of Hermite-Hadamard inequality using s−convex functions in the 2nd sense. For this purpose we used some special inequalities like Hölder’s. Publisher's Version

In this study, we first establish two Hermite-Hadamard type inequality for multiplicative (geometric) Riemann-Liouville fractional integrals. Then, by using some properties of multiplicative convex function, we give some new inequalities involving multiplicative fractional integrals. WOS:000541509200006 2-s2.0-85089493148