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Constructions of Uniformly Convex Functions
"... Abstract. We give precise conditions under which the composition of a norm with a convex function yields a uniformly convex function on a Banach space. Various applications are given to functions of power type. The results are dualized to study uniform smoothness and several examples are provided. ..."
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Cited by 2 (1 self)
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Abstract. We give precise conditions under which the composition of a norm with a convex function yields a uniformly convex function on a Banach space. Various applications are given to functions of power type. The results are dualized to study uniform smoothness and several examples are provided.
On the CoOrdinated Convex Functions
, 2014
"... Abstract: In this paper, some new integral inequalities are given for convex functions on the coordinates. By using wellknown classical inequalities and a new integral identity (Lemma 1), we obtain some general results for coordinated convex functions. ..."
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Abstract: In this paper, some new integral inequalities are given for convex functions on the coordinates. By using wellknown classical inequalities and a new integral identity (Lemma 1), we obtain some general results for coordinated convex functions.
Extremal approximately convex functions . . .
, 1998
"... A real valued function f defined on a convex K is an approximately convex function iff it satisfies x + y f(x) + f(y) ..."
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A real valued function f defined on a convex K is an approximately convex function iff it satisfies x + y f(x) + f(y)
Minimization of an Mconvex Function
 Discrete Appl. Math
, 1998
"... We study the minimization of an Mconvex function introduced by Murota. It is shown that any vector in the domain can be easily separated from a minimizer of the function. Based on this property, we develop a polynomial time algorithm. Keywords: matroid, base polyhedron, convex function, minimizatio ..."
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Cited by 12 (7 self)
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We study the minimization of an Mconvex function introduced by Murota. It is shown that any vector in the domain can be easily separated from a minimizer of the function. Based on this property, we develop a polynomial time algorithm. Keywords: matroid, base polyhedron, convex function
MINIMALIST APPROXIMATIONS FOR CONVEX FUNCTIONS
"... We study data structures for approximating convex functions whose slopes are bounded as well as applications of such data structures to problems in clustering and facility location. ..."
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We study data structures for approximating convex functions whose slopes are bounded as well as applications of such data structures to problems in clustering and facility location.
AN EXTENSION PROBLEM FOR CONVEX FUNCTIONS.
, 806
"... ABSTRACT. We give a statement on extension with estimates of convex functions defined on a linear subspace, inspired by similar extension results concerning metrics on positive line bundles. 1. ..."
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ABSTRACT. We give a statement on extension with estimates of convex functions defined on a linear subspace, inspired by similar extension results concerning metrics on positive line bundles. 1.
CERTAIN INEQUALITIES FOR CONVEX FUNCTIONS
, 2005
"... ABSTRACT. Classical inequalities like Jensen and its reverse are used to obtain some elementary numerical inequalities for convex functions. Furthermore, imposing restrictions on the data points several new constrained inequalities are given. ..."
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ABSTRACT. Classical inequalities like Jensen and its reverse are used to obtain some elementary numerical inequalities for convex functions. Furthermore, imposing restrictions on the data points several new constrained inequalities are given.
APPROXIMATE CONVEX FUNCTIONS
"... Abstract. The purpose of this paper is to study a class of generalized convex functions defined on a Banach space X, called approximate convex functions which are stable under finite sums and finite suprema, and for which most of the known subdifferentials such as the Clarke, the Mordukhovich and th ..."
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Cited by 4 (0 self)
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Abstract. The purpose of this paper is to study a class of generalized convex functions defined on a Banach space X, called approximate convex functions which are stable under finite sums and finite suprema, and for which most of the known subdifferentials such as the Clarke, the Mordukhovich
ON THE CHARACTERIZATION OF CONVEX FUNCTIONS
"... Abstract. A simple characterization of convex functions as indefinite integrals of nondecreasing ones is obtained, using only Riemann integrals. Characterization of convex functions ([3], App. III, theor. 2) is usually performed within Lebesgue’s integration theory, despite the fact that the invo ..."
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Abstract. A simple characterization of convex functions as indefinite integrals of nondecreasing ones is obtained, using only Riemann integrals. Characterization of convex functions ([3], App. III, theor. 2) is usually performed within Lebesgue’s integration theory, despite the fact
On the continuity of biconjugate convex functions
 PROC. AMER. MATH. SOC
, 2001
"... We show that a Banach space is a Grothendieck space if and only if every continuous convex function on X has a continuous biconjugate function on X ∗ ∗ , thus also answering a question raised by S. Simons. Related characterizations and examples are given. ..."
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We show that a Banach space is a Grothendieck space if and only if every continuous convex function on X has a continuous biconjugate function on X ∗ ∗ , thus also answering a question raised by S. Simons. Related characterizations and examples are given.
Results 11  20
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11,544