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ON CONVEX FUNCTIONS IN AN
"... Abstract. In this note we define the notions of convexity for analytic functions in the ellipse E = z = x+ iy ∈ C: x ..."
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Abstract. In this note we define the notions of convexity for analytic functions in the ellipse E = z = x+ iy ∈ C: x
ON STRONGLY hCONVEX FUNCTIONS
, 2011
"... We introduce the notion of strongly hconvex functions (defined on a normed space) and present some properties and representations of such functions. We obtain a characterization of inner product spaces involving the notion of strongly hconvex functions. Finally, a Hermite–Hadamard–type inequality ..."
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Cited by 4 (0 self)
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We introduce the notion of strongly hconvex functions (defined on a normed space) and present some properties and representations of such functions. We obtain a characterization of inner product spaces involving the notion of strongly hconvex functions. Finally, a Hermite–Hadamard–type inequality
Convex Functions and Spacetime Geometry
, 2000
"... Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime (M, gµν) or an initial data set (Σ, hij, Kij) admitting a suitably defined convex function. We ..."
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Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime (M, gµν) or an initial data set (Σ, hij, Kij) admitting a suitably defined convex function. We
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5396 (68 self)
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long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinitedimensional function spaces. A major theme
Convex Functions On The Heisenberg Group
 Calc. Var. Partial Differential Equations
"... Convex functions in Euclidean space can be characterized as universal viscosity subsolutions of all homogeneous fully nonlinear second order elliptic partial di#erential equations. This is the starting point we have chosen for a theory of convex functions on the Heisenberg group. 1. ..."
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Cited by 23 (2 self)
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Convex functions in Euclidean space can be characterized as universal viscosity subsolutions of all homogeneous fully nonlinear second order elliptic partial di#erential equations. This is the starting point we have chosen for a theory of convex functions on the Heisenberg group. 1.
Convex Functions on Time Scales
"... Abstract. We define the notion of a convex function on time scales. Some results connecting this notion with the notion of convex function on a classic interval and convex sequences are also included. We also define the subdifferential of a convex function on time scale and present some properties r ..."
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Abstract. We define the notion of a convex function on time scales. Some results connecting this notion with the notion of convex function on a classic interval and convex sequences are also included. We also define the subdifferential of a convex function on time scale and present some properties
On the subdijferentiability of convex functions
 Bull. Amer. Math. Soc
, 1965
"... Each lower semicontinuous proper convex function f on a Banach space E defines a certain multivalued mapping of from E to E * called the subdifferential of f. It is shown here that the mappings arising this way are precisely the ones whose graphs are maximal "cyclically monotone " relatio ..."
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Cited by 84 (2 self)
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Each lower semicontinuous proper convex function f on a Banach space E defines a certain multivalued mapping of from E to E * called the subdifferential of f. It is shown here that the mappings arising this way are precisely the ones whose graphs are maximal "cyclically monotone "
Geometrically Relative Convex Functions
, 2014
"... Abstract: In this paper, some new concepts of geometrically relative convex sets and relative convex functions are defined. These new classes of geometrically relative convex functions unify several known and new classes of relative convex functions such as exponential convex functions. New Hermite ..."
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Cited by 1 (1 self)
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Abstract: In this paper, some new concepts of geometrically relative convex sets and relative convex functions are defined. These new classes of geometrically relative convex functions unify several known and new classes of relative convex functions such as exponential convex functions. New Hermite
Convex functions on discrete sets
 In Klette and Žunić (2004
, 2004
"... Abstract. We propose definitions of digital convex sets and digital convex functions and relate them to a refined definition of digital hyperplanes. ..."
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Cited by 6 (2 self)
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Abstract. We propose definitions of digital convex sets and digital convex functions and relate them to a refined definition of digital hyperplanes.
Convex functions on Carnot groups
 Rev. Mat. Iberoam
"... Abstract. We consider the definition and regularity properties of convex functions in Carnot groups. We show that various notions of convexity in the subelliptic setting that have appeared in the literature are equivalent. Our point of view is based on thinking of convex functions as subsolutions of ..."
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Cited by 13 (1 self)
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Abstract. We consider the definition and regularity properties of convex functions in Carnot groups. We show that various notions of convexity in the subelliptic setting that have appeared in the literature are equivalent. Our point of view is based on thinking of convex functions as subsolutions
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