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The authors of the paper propose a new method of investigation of an an equality for the case of twice-differentiable convex functions with respect to the conformable fractional integrals. With the help of this equality, we establish several Simpson-type inequalities for twice-differentiable convex functions by using conformable fractional integrals. Sundry significant inequalities are obtained by taking advantage of the convexity, the Hölder inequality, and the power mean inequality. By using the specific selection of our results, we give several new and well-known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we first obtain two weighted identities for twice partially differentiable mappings. Moreover, utilizing these equalities,swtreaecstta.blish the weighted Hermite-Hadamard type inequalities and weighted Simpson type inequalities for co-ordinated convex functions in a rectangle from the plane R2, respectively. The results given in this paper provide generalizations of some result established in earlier works. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to show that under reasonable assumptions Debrunner and Flor Theorem can be extended to arbitrary θ-monotone operators. This generalization provides some tools for further analysis of the θ-monotone operators, which allows us for establishing some key facts related to domains and ranges of θ-maximal monotone operators. [ABSTRACT FROM AUTHOR]

In this paper, several integral inequalities for the functions whose derivatives are s-convex functions in the fourth sense are obtained by means of Caputo fractional derivative and Caputo-Fabrizio integral operator. Also the Hermite-Hadamard type inequalities for s-convex functions and their products are stated via Caputo-Fabrizio integral operator. [ABSTRACT FROM AUTHOR]

In this paper, we present new integral results on fractional order inequalities involving convex functions using MarichevSaigo-Maeda integral operators. Using the same integral approach, other fractional integral inequalities for positive and continuous functions are also proved. The obtained results can be seen as a new contribution in inequality theory by means of Marichev-Saigo-Maieda approach. [ABSTRACT FROM AUTHOR]

In 1964, Levinson [4] proved integral inequalities concerning generalization of Hardy's inequalities. In this paper two results are given. First one is extension of the Levinson Integral inequalities via convexity and the second is for the Levinson Integral inequalities of Hardy, this inequalities are established for p < 1 and some related inequalities are also considered with a sharp constant. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to define a new class of analytic, normalized functions in the open unit disk D = fz: z 2 C and jzj < 1g subordinating with crescent shaped regions, and to derive certain coe fficient estimates a2, a3 and Fekete-Szegö inequality for f 2Mq(α; β; λ). A similar result have been done for the function f-1: Further application of our results to certain functions defined by convolution products with a normalized analytic function is given, in particular we obtain Fekete-Szegö inequalities for certain subclasses of functions defined through Poisson distribution series. [ABSTRACT FROM AUTHOR]

In this paper, we present a general version of operator Bellman inequality. Also, the refinement of inequality due to J. Aujla and F. Silva for the convex functions is given as well. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of semi-infinite optimization with nonsmooth data. We introduce the Arrow-Hurwitcz-Uzawa constraint qualification which is based on the Clarke subdifferential. Then, we derive a suitable Karush-Kuhn-Tucker type necessary optimality condition. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper we establish a refinement and some reverses for Jensen's inequality for the general Lebesgue integral on divisions of measurable space. Applications for discrete inequalities and weighted means of positive numbers are also given. Some examples related to Hermite-Hadamard inequality for convex functions are provided as well. [ABSTRACT FROM AUTHOR]

This work furnishes some Hadamard-Hermite (HH) type inequalities for interval-valued function by using an efficient partial order CW on the space of all compact intervals. It has been shown that the interval-valued HH's inequality proved herein, applied to already determined inequalities for real-valued functions. Specifically, this paper unifies and generalizes HH inequalities in the literature. We illustrate results with numerical examples. [ABSTRACT FROM AUTHOR]

This paper is mainly devoted to studying operator Jensen inequality. More precisely, a new generalization of Jensen inequality and its reverse version for convex (not necessary operator convex) functions have been proved. Several special cases are discussed as well. [ABSTRACT FROM AUTHOR]

In this paper, some new inequalities for generalized convex functions are obtained. Some applications for some generalized special means are also given. [ABSTRACT FROM AUTHOR]

We study the existence and uniqueness of solutions of a class of Quantum Stochastic Evolution Equations (QSEEs) defined on a locally convex space whose topology is generated by a family of seminorms defined via the norm of the range space of the operator processes. These solutions are called strong solutions in comparison with the solutions of similar equations defined on the space of operator processes where the topology is generated by the family of seminorms defined via the inner product of the range space. The evolution operator generates a bounded semigroup. We show that under some more general conditions, the unique solution is stable. These results extend some existing results in the literature concerning strong solutions of quantum stochastic differential equations. [ABSTRACT FROM AUTHOR]

We investigate the existence of solution for a fractional integro-differential inclusion via the Caputo-Hadamard fractional derivation. We prove that dimension of the set of solutions for the inclusion problem is infinite dimensional under some conditions. [ABSTRACT FROM AUTHOR]

A new class of contraction pairs in uniformly convex metric spaces is introduced. The coincidence and best proximity points of this class of mappings is studied, and finally, illustrative examples are given to support the new results. [ABSTRACT FROM AUTHOR]

Using the concept of ν-convex functions as generalization of convex functions, we inquiry about the relation between minimization problem and Kuhn-Tucker problem with new settings and give sufficient and necessary optimality condition. Also the relation between minimization problem and it's Mond-Weir dual problem in ν-convex case is investigated. [ABSTRACT FROM AUTHOR]