This paper presents enhanced parameterized quantum Hermite-Hadamard type integral inequalities for functions whose third right and left q-derivatives in absolute value are strongly convex functions. We obtain new boun...
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This paper presents enhanced parameterized quantum Hermite-Hadamard type integral inequalities for functions whose third right and left q-derivatives in absolute value are strongly convex functions. We obtain new bounds using Holder's and power mean inequalities as primary tools. Also, we derive new quantum estimates for q-trapezoidal and q-midpoints type inequalities in specific scenarios, which we illustrate with examples. These outcomes possess the potential for practical applications in optimizing various economic problems.
The notion of strongly n-convexfunctions with modulus c > 0 is introduced and investigated. Relationships between such functions and n-convexfunctions in the sense of Popoviciu as well as generalized convex funct...
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The notion of strongly n-convexfunctions with modulus c > 0 is introduced and investigated. Relationships between such functions and n-convexfunctions in the sense of Popoviciu as well as generalized convexfunctions in the sense of Beckenbach are given. Characterizations by derivatives are presented. Some results on strongly Jensen n-convexfunctions are also given. (C) 2010 Elsevier Ltd. All rights reserved.
The aim of this paper is to find a convenient and practical method to approximate a given real-valued function of multiple variables by linear operators, which approximate all strongly convex functions from above (or ...
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The aim of this paper is to find a convenient and practical method to approximate a given real-valued function of multiple variables by linear operators, which approximate all strongly convex functions from above (or from below). Our main contribution is to use this additional knowledge to derive sharp error estimates for continuously differentiable functions with Lipschitz continuous gradients. More precisely, we show that the error estimates based on such operators are always controlled by the Lipschitz constants of the gradients, the convexity parameter of the strong convexity and the error associated with using the quadratic function, see Theorems 3.1 and 3.3. Moreover, assuming the function, we want to approximate, is also stronglyconvex, we establish sharp upper as well as lower refined bounds for the error estimates, see Corollaries 3.2 and 3.4. As an application, we define and study a class of linear operators on an arbitrary polytope, which approximate strongly convex functions from above. Finally, we present a numerical example illustrating the proposed method. (C) 2014 Elsevier Inc. All rights reserved.
In this paper we use basic properties of strongly convex functions to obtain new inequalities including Jensen type and Jensen-Mercer type inequalities. Applications for special means are pointed out as well. We also ...
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In this paper we use basic properties of strongly convex functions to obtain new inequalities including Jensen type and Jensen-Mercer type inequalities. Applications for special means are pointed out as well. We also give a Jensen's operator inequality for strongly convex functions. As a corollary, we improve the Holder-McCarthy inequality under suitable conditions. More precisely we show that if Sp (A) subset of (1, infinity), then < Ax, x >(r) <= < A(r)x, x > - r(2) - r/2 (< A(2)x, x > - < Ax, x >(2)), r >= 2 and if Sp (A) subset of (0, 1), then < A(r)x, x > <= < Ax, x >(r) + r - r(2)/2 (< Ax, x >(2) - < A(2)x, x >), 0 < r < 1 for each positive operator A and x is an element of H with parallel to x parallel to = 1.
A known family of fractional integral operators ( with the Gauss hypergeometric function in the kernel) is used here to define some new subclasses of strongly starlike and strongly convex functions of order beta and t...
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A known family of fractional integral operators ( with the Gauss hypergeometric function in the kernel) is used here to define some new subclasses of strongly starlike and strongly convex functions of order beta and type alpha in the open unit disk U. For each of these new function classes, several inclusion relationships associated with the fractional integral operators are established. Some interesting corollaries and consequences of the main inclusion relationships are also considered.
Counterparts of the converse Jensen inequality for stronglyconvex and strongly midconvexfunctions are presented. The Jessen inequality and converse Jessen inequality (involving linear positive normalized functionals...
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Counterparts of the converse Jensen inequality for stronglyconvex and strongly midconvexfunctions are presented. The Jessen inequality and converse Jessen inequality (involving linear positive normalized functionals) for strongly convex functions are also given. (C) 2015 Elsevier Inc. All rights reserved.
In this paper, we obtain some Jensen's and Hermite-Hadamard's type inequalities for lower, upper, and strongly convex functions defined on convex subsets in normed linear spaces. The case of inner product spac...
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In this paper, we obtain some Jensen's and Hermite-Hadamard's type inequalities for lower, upper, and strongly convex functions defined on convex subsets in normed linear spaces. The case of inner product space is of interest since in these case the concepts of lower convexity and strong convexity coincides. Applications for univariate functions of real variable and the connections with earlier Hermite-Hadamard's type inequalities are also provided.
Some properties of strongly convex functions are presented. A characterization of pairs of functions that can be separated by a stronglyconvex function and a Hyers-Ulam stability result for strongly convex functions ...
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Some properties of strongly convex functions are presented. A characterization of pairs of functions that can be separated by a stronglyconvex function and a Hyers-Ulam stability result for strongly convex functions are given. An integral Jensen-type inequality and a Hermite-Hadamard-type inequality for strongly convex functions are obtained. Finally, a relationship between strong convexity and generalized convexity in the sense of Beckenbach is shown.
This paper is about the minimization of Lipschitz-continuous and strongly convex functions over integer points in polytopes. Our results are related to the rate of convergence of a black-box algorithm that iteratively...
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This paper is about the minimization of Lipschitz-continuous and strongly convex functions over integer points in polytopes. Our results are related to the rate of convergence of a black-box algorithm that iteratively solves special quadratic integer problems with a constant approximation factor. Despite the generality of the underlying problem, we prove that we can find efficiently, with respect to our assumptions regarding the encoding of the problem, a feasible solution whose objective function value is close to the optimal value. We also show that this proximity result is the best possible up to a factor polynomial in the encoding length of the problem.
The study of fractional integral inequalities has attracted the interests of many researchers due to their potential applications in various fields. Estimates obtained via strongly convex functions produce better and ...
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The study of fractional integral inequalities has attracted the interests of many researchers due to their potential applications in various fields. Estimates obtained via strongly convex functions produce better and sharper bounds when compared to convexfunctions. To this end, we establish some new Hermite-Hadamard and Fejer types inequalities by means of the Caputo-Fabrizio fractional integral operators for strongly convex functions. In particular, we prove among other things that if omega : I -> R is a stronglyconvex function with modulus c > 0 and alpha, beta is an element of I with alpha 0 is a normalization function. Some applications to special means have also been investigated.,
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