In this article, starting with an equation for weighted integrals, we obtained several extensions of the well-known Hermite-Hadamard inequality. We used generalized weighted integral operators, which contain the Riema...
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In this article, starting with an equation for weighted integrals, we obtained several extensions of the well-known Hermite-Hadamard inequality. We used generalized weighted integral operators, which contain the Riemann-Liouville and the k-Riemann-Liouville fractional integral operators. The functions for which the operators were considered satisfy various conditions such as the h-convexity, modified h-convexity and s-convexity.
In this paper, using a new identity, we establish some new quantum of Simpson like type inequalities for functions whose q-derivatives are convex. Applications of the results are also given.
In this paper, using a new identity, we establish some new quantum of Simpson like type inequalities for functions whose q-derivatives are convex. Applications of the results are also given.
A short, self-contained method to produce quantitative C1,alpha loc-es-timates for convex functions in terms of the quasi-symmetric property of their associated Bregman divergences is presented.
A short, self-contained method to produce quantitative C1,alpha loc-es-timates for convex functions in terms of the quasi-symmetric property of their associated Bregman divergences is presented.
Our main purpose in this paper is to obtain certain sharp estimates of the third Hankel determinant for the class F of Ozaki close-to-convex functions. This class was introduced by Ozaki in 1941. functions in F are no...
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Our main purpose in this paper is to obtain certain sharp estimates of the third Hankel determinant for the class F of Ozaki close-to-convex functions. This class was introduced by Ozaki in 1941. functions in F are not necessarily starlike but are convex in one direction and so are close-to-convex. We prove that the sharp bounds of Script capital H3,1(f) and Script capital H3,1(f-1) for f is an element of F are all equal to 1/16. We also calculate the sharp bounds of the third Hankel determinant with entry of coefficients on the inverse of convex functions.
In this paper sharp bounds of the third Hankel determinant for starlike and convex functions related to the exponential function are obtained, thus solving two long-standing open problems.
In this paper sharp bounds of the third Hankel determinant for starlike and convex functions related to the exponential function are obtained, thus solving two long-standing open problems.
Various integral inequalities for s-convex functions in the second sense are obtained by means of the Caputo fractional derivative and the Caputo-Fabrizio integral operator. Some generalizations of the Hermite-Hadamar...
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Various integral inequalities for s-convex functions in the second sense are obtained by means of the Caputo fractional derivative and the Caputo-Fabrizio integral operator. Some generalizations of the Hermite-Hadamard type inequalities including the Caputo-Fabrizio integral operator are expressed for the functions whose derivatives are s-convex. Moreover, some inequalities involving these fractional operators are stated for the product of these functions. Inequalities involving special means and the digamma function are given as applications.
In this study, we use the properties of convex functions, Jensen’s inequality, Holder’s inequality, and the chain rule to establish a new class of dynamic Hardy-type inequalities on time scales using delta calculus....
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In this paper we introduce some subclasses of normalized univalent functions, more exactly subclasses of S-star, which we will call convex functions of degree n. The main tool used is the idea behind Alexander's d...
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In this paper we introduce some subclasses of normalized univalent functions, more exactly subclasses of S-star, which we will call convex functions of degree n. The main tool used is the idea behind Alexander's duality theorem between S-star and K. Also, we present a necessary and sufficient condition for convexity of degree n in two complex variables.
In this paper we deal with functions related to generalized convexity and refine Jensen type inequalities satisfied by such functions. Specifically, we extend inequalities satisfied by uniformly convex functions, stro...
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In this paper we deal with functions related to generalized convexity and refine Jensen type inequalities satisfied by such functions. Specifically, we extend inequalities satisfied by uniformly convex functions, strongly convex functions as well as superquadratic functions.
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