In this paper, we initially present new some inequality of Hermite-Hadamard-type for co-ordinated convex functions on a rectangle from the plane (2) via Riemann-Liouville fractional integrals. Then, we give an integra...
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In this paper, we initially present new some inequality of Hermite-Hadamard-type for co-ordinated convex functions on a rectangle from the plane (2) via Riemann-Liouville fractional integrals. Then, we give an integral identity for fractional integrals and with the help of this integral identity we establish some integral inequalities with the right-hand side of the fractional Hermite-Hadamard-type inequality on the co-ordinates.
In the article, we establish an inequality for Csiszar divergence associated with s-convex functions, present several inequalities for Kullback-Leibler, Renyi, Hellinger, Chi-square, Jeffery's, and variational dis...
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In the article, we establish an inequality for Csiszar divergence associated with s-convex functions, present several inequalities for Kullback-Leibler, Renyi, Hellinger, Chi-square, Jeffery's, and variational distance divergences by using particular s-convex functions in the Csiszar divergence. We also provide new bounds for Bhattacharyya divergence.
Rockafellar proved that any closed, convex function is uniquely determined by its subdifferential mapping up to an additive constant. The aim of this article is to provide an elementary proof of the same result.
Rockafellar proved that any closed, convex function is uniquely determined by its subdifferential mapping up to an additive constant. The aim of this article is to provide an elementary proof of the same result.
The problem of minimization of a convex nonsmooth function in a finite-dimensional space is considered. The method employs the Moreau-Yosida regularization. To accelerate the computation process, the proximate functio...
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The problem of minimization of a convex nonsmooth function in a finite-dimensional space is considered. The method employs the Moreau-Yosida regularization. To accelerate the computation process, the proximate function is constructed using quasi-Newton matrices.
The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar's constraint qualification holds. In this pape...
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The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that Rockafellar's constraint qualification holds. In this paper, we prove the maximal monotonicity of A + partial derivative f provided that A is a maximally monotone linear relation, and f is a proper lower semicontinuous convex function satisfying dom A boolean AND int dom partial derivative f not equal circle divide. Moreover, A + partial derivative f is of type (FPV). The maximal monotonicity of A + partial derivative f when int dom A boolean AND dom partial derivative f not equal circle divide follows from a result by Verona and Verona, which the present work complements.
We show that for every closed convex set C in a separable Banach space X there is a C-infinity-smooth convex function f : X--> [0, infinity) so that f(-1) (0) = C. We also deduce some interesting consequences conce...
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We show that for every closed convex set C in a separable Banach space X there is a C-infinity-smooth convex function f : X--> [0, infinity) so that f(-1) (0) = C. We also deduce some interesting consequences concerning smooth approximation of closed convex sets and continuous convex functions.
Complying with the existing buffer operator of grey system theory axiom system, using the relevant properties of convex function, and combining with strengthening buffer operator, the paper constructs a new class of s...
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ISBN:
(纸本)9781457706530
Complying with the existing buffer operator of grey system theory axiom system, using the relevant properties of convex function, and combining with strengthening buffer operator, the paper constructs a new class of strengthening buffer operator and gives the proof. It makes the new strengthening buffer operator which is based on the original application further extended.
This paper develops an algorithm, for estimating the parameters in a general multiple regression model. The estimator coincides with the maximum likelihood estimator when the errors have a probability density function...
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