M. Emin Ozdemir, Alper Ekinci, Ahmet Ocak Akdemir
In this study, we obtain some new integral inequalities for different classes of convex functions by using some elementary inequalities and classical inequalities like general Cauchy inequality and Minkowski inequality.
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We establish some monotonicity results and functional inequalities for modified Lommel functions of the first kind. In particular, we obtain new Turán type inequalities and bounds for ratios of modified Lommel functions of the first kind, as well as the function itself. These results complement and in some cases improve on existing results, and also generalise a number of the results from the literature on monotonicity patterns and functional inequalities for the modified Struve function of the first kind.
In this paper, we establish two new convex dominated function and then we obtain new Hadamard type inequalities related to this denitions.
In this paper, we obtain inequalities for some integrals involving the modified Lommel function of the first kind $t_{μ,ν}(x)$. In most cases, these inequalities are tight in certain limits. We also deduce a tight double inequality, involving the modified Lommel function $t_{μ,ν}(x)$, for a generalized hypergeometric function. The inequalities obtained in this paper generalise recent bounds for integrals involving the modified Struve function of the first kind.
In this paper, we establish some Simpson type inequalities for functions whose third derivatives in the absolute value are h-convex and (α,m)-convex, respectively.
In this paper, we obtain some new inequalities for functions whose second derivatives' absolute value is s-convex and log-convex. Also, we give some applications for numerical integration.
In this paper we deduce some tight Turán type inequalities for Tricomi confluent hypergeometric functions of the second kind, which in some cases improve the existing results in the literature. We also give alternative proofs for some already established Turán type inequalities. Moreover, by using these Turán type inequalities, we deduce some new inequalities for Tricomi confluent hypergeometric functions of the second kind. The key tool in the proof of the Turán type inequalities is an integral representation for a quotient of Tricomi confluent hypergeometric functions, which arises in the st…
We obtain new inequalities for the modified Bessel function of the second kind $K_ν$ in terms of the gamma function. These bounds follow as special cases of inequalities that we derive for the kernel of the Krätzel integral transformation.
Some inequalities for different types of convexity are established.
We present Hermite--Hadamard type inequalities for Wright-convex, strongly convex and strongly Wright-convex functions of several variables defined on simplices
In this study, the author establish some inequalities of Hadamard like based on convex and s-convexity in the second sense. Some applications to special means of positive real numbers are also given.
Simple inequalities for some integrals involving the modified Struve function of the first kind $\mathbf{L}_ν(x)$ are established. In most cases, these inequalities have best possible constant. We also deduce a tight double inequality, involving the modified Struve function $\mathbf{L}_ν(x)$, for a generalized hypergeometric function.
We have recently established some integral inequalities for convex functions via the Hermite-Hadamard's inequalities. In continuation here, we also establish some interesting new integral inequalities for convex functions via the Hermite--Hadamard's inequalities and Jensen's integral inequality. Useful applications involving special means are also included.
Inequalities play an important role in pure and applied mathematics. In particular, Jensen's inequality, one of the most famous inequalities, plays a main role in the study of the existence and uniqueness of initial and boundary value problems for differential equations. In this work we prove some new Jensen-type inequalities for $m$-convex functions, and we apply them to generalized Riemann-Liouville-type integral operators. It is remarkable that, if we consider $m=1$, we obtain new inequalities for convex functions.
In this paper, we establish some new integral inequalities for for m- and (alpha,m)-logarithmically convex functions.
This is a survey paper concerning some theorems on stochastic convex ordering and their applications to functional inequalities for convex functions. We present the recent results on those subjects
The author introduce the concept of harmonically convex functions and establish some Hermite-Hadamard type inequalities of these classes of functions
In this paper, the author established Hermite-Hadamard's inequalities for harmonically convex functions via fractional integrals and obtained some Hermite-Hadamard type inequalities of these classes of functions.
In this paper, we establish Ostrowski's type inequalities for strongly-convex functions where c>0 by using some classical inequalities and elemantery analysis. We also give some results for product of two strongly-convex functions.
In this paper, we establish several inequalities for s-convex mappings that are connected with the Riemann-Liouville fractional integrals. Our results have some relationships with certain integral inequalities in the literature.
In this paper, we establish several new inequalities for twice differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.
In this paper, we establish some integral ineuqalities for n- times differentiable convex functions.
The author introduces the concept of harmonically (α,m)-convex functions and establishes some Hermite-Hadamard type inequalities of these classes of functions.
In this paper, new integral inequalities of Hadamard type involving several differentiable Φ-r-convex functions are given.
In this paper, a new class of convex functions as a generalization of convexity which is called (h-m)-convex functions and some properties of this class is given. We also prove some Hadamard's type inequalities.
In this paper, the notation of strongly log-convex functions with respect to c>0 is introduced and versions of Hermite Hadamard-type inequalities for strongly logarithmic convex functions are established.
In this paper, the author introduces the concept of the quasi-geometrically convex and defines a new identity for fractional integrals. By using of this identity, author obtains new estimates on generalization of Hadamard, Ostrowski and Simpson type inequalities for GA-s-convex, quasi-geometrically convex and (s,m)-GA-convex functions via Riemann Liouville fractional integral.
The author introduces the concept of harmonically s-convex functions and establishes some Ostrowski type inequalities and Hermite-Hadamard type inequality of these classes of functions.
In this paper, we prove some new inequalities of Hadamard-type for convex functions on the co-ordinates.
We have made some new definitions using the inequalities of Young' and Nesbitt'. And we have given some features of these new definitions. After, we established new Hadamard type inequalities for convex functions in the Young and Nesbitt sense.
In this paper, we establish (presumably new type) integral inequalities for convex functions via the Hermite--Hadamard's inequalities. As applications, we apply these new inequalities to construct inequalities involving special means of real numbers, some error estimates for the formula midpoint are given. Finally, new inequalities for some special and $q-$special functions are also pointed out.
In this paper, we established some new inequalities via s-convex and s-concave functions.
In this paper, we prove some new inequalities of Hadamard-type for s-convex functions on the co-ordinates.
In this paper, the Authors establish a new identity for differentiable functions. By the well-known Hölder and power mean inequality, they obtain some integral inequalities related to the convex functions and apply these inequalities to special means.
In this paper, some new inequalities of Ostrowski type established for the class of m- and (alpha,m)-geometrically convex functions which are generalizations of geometric convex functions.
New identity for fractional integrals have been defined. By using of this identity, we obtained new estimates on generalization of Hadamard, Ostrowski and Simpson type inequalities for s-convex, quasi-convex, m-convex functions via Riemann Liouville fractional integral.
In this paper, we establish some integral ineuqalities for n- times differentiable quasi-convex functions.
In this paper, The author introduces the concepts of the GA-s-convex functions in the first sense and second sense and establishes some integral inequalities of Hermite-Hadamard type related to the GA-s-convex functions.
In this paper some Hadamard-type inequalities for convex functions of 3-variables on a rectanguler box are given. We also define a mapping related to convex functions on a rectanguler box.
In the paper, the authors establish some new Hermite-Hadamard type inequalities for functions whose first derivatives are of convexity and apply these inequalities to construct inequalities of special means.
In this paper, some new inequalities of the Hermite-Hadamard type for h-convex functions via Riemann-Liouville fractional integral are given.
In this paper some Hadamard_type inequalities for product of convex functions of 2-variables on the co-ordinates are given.
On Hadamard-Type Inequalities for Co-ordinated r-Convex Functions
该研究定义了坐标意义下的r-凸性概念，并推导得到了若干对应的Hadamard型不等式，丰富了凸函数不等式领域的相关结论。
In this paper we obtained some new Hadamard-Type inequalities for functions whose derivatives absolute values m-convex. Some applications to special means of real numbers are given.
In this paper, it is a fuction that is a GA-convex differentiable for a new identity. As a result of this identity, some new and general integral inequalities for differentiable GA-convex functions are obtained.
In this work, new inequalities connected with the Steffensen's integral inequality for s-convex functions are proved
In this paper, the authors establish a new type integral inequalities for differentiable s-convex functions in the second sense. By the well-known Hölder inequality and power mean inequality, they obtain some integral inequalities related to the s-convex functions and apply these inequalities to special means for positive real numbers.
In this paper, we obtained some new estimates on generalization of Hadamard, Ostrowski and Simpson-like type inequalities for harmonically quasi-convex functions via Riemann Liouville fractional integral.
In this paper, we obtain some Simpson type inequalities for functions whose derivatives in absolute value are m- and (alpha,m)- logarithmically convex functions.
In this paper, we obtain some new integral inequalities like Hermite-Hadamard type for third derivatives absolute value are log-convex. We give some applications to quadrature formula for midpoint error estimate.
In this paper, we establish some new Ostrowski's type inequalities for m- and (alpha,m)- logarithmically convex functions by using the Riemann-Liouville fractional integrals.
In this paper, approximate lower and upper Hermite--Hadamard type inequalities are obtained for functions that are approximately convex with respect to a given Chebyshev system.
In this paper, we introduce the notion of (g,Φ_{h})-convex dominated function and present some properties of them. Finally, we present a version of Hermite-Hadamard-type inequalities for (g,Φ_{h})-convex dominated functions. Our results generalize the Hermite-Hadamard-type inequalities in [2], [4] and [6].
Some Turán type inequalities for Struve functions of the first kind are deduced by using various methods developed in the case of Bessel functions of the first and second kind. New formulas, like Mittag-Leffler expansion, infinite product representation for Struve functions of the first kind, are obtained, which may be of independent interest. Moreover, some complete monotonicity results and functional inequalities are deduced for Struve functions of the second kind. These results complement naturally the known results for a particular case of Lommel functions of the first kind, and for modifi…
In this paper certain Turán type inequalities for some Lommel functions of the first kind are deduced. The key tools in our proofs are the infinite product representation for these Lommel functions of the first kind, a classical result of G. Pólya on the zeros of some particular entire functions, and the connection of these Lommel functions with the so-called Laguerre-Pólya class of entire functions. Moreover, it is shown that in some cases J. Steinig's results on the sign of Lommel functions of the first kind combined with the so-called monotone form of l'Hospital's rule can be used in the pr…
In the paper, the authors introduce a new concept "extended $s$-convex functions", establish some new integral inequalities of Hermite-Hadamard type for this kind of functions, and apply these inequalities to derive some inequalities of special means.
In this paper, we first prove two new identities for multiplicative differentiable functions. Based on this identity, we establish a midpoint and trapezoid type inequalities for multiplicatively convex functions. Applications to special means are also given.
In this paper, some new integral inequalities of Hermite-Hadamard type related to the s-geometrically convex functions are established and some applications to special means of positive real numbers are also given.
In this paper, we obtain new estimates on generalization of Hermite-Hadamard, Simpson and Ostrowski type inequalities for functions whose second derivatives is $φ$-convex via fractional integrals.
Authors introduce the concept of harmonically $(s,m)$-convex functions in second sense in \cite{II}.In this article, we establish some Hermite-Hadamard type inequalities of this class of functions.
In this paper we establish Hermite-Hadamard type inequalities for mappings whose derivatives are s-convex in the second sense and concave.
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