Results 11 to 20 of about 4,236,155 (127)
Jensen-Type Inequalities for Invex Functions [PDF]
, 1999 Jensen's inequality for a real convex function f on a convex domain is generalised in several ways to vector functions with a cone inequality, and to invex functions generalizing convex ...
Craven, Bruce Desmond, Dragomir, Sever S
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Asymptotic behaviour of the solution of a functional-differential equation [PDF]
, 1984 The asymptotic behaviour as t→∞ of the solution of the functional- differential equation y'(t) = -y(t/k), with y(0) = 1 and k > 1 , is derived from an integral representation by the method of steepest descents.
Tripp, CE
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A Converse of the Jensen Inequality for Convex Mappings of Several Variables and Applications [PDF]
, 1999 In this paper we point out a converse result of the celebrated Jensen inequality for differentiable convex mappings of several variables and apply it to counterpart well-known analytic inequalities. Applications to Shannon's and Rényi's entropy mappings
Dragomir, Sever S
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On the stability of Jensen’s functional equation on groups [PDF]
Proceedings Mathematical Sciences, 2007 In this paper we establish the stability of Jensen's functional equation on some classes of groups. We prove that Jensen equation is stable on noncommutative groups such as metabelian groups and $T(2, K)$, where $K$ is an arbitrary commutative field with characteristic different from two. We also prove that any group $A$ can be embedded into some group
Faĭziev, Valeriĭ A. +1 more
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On a Jensen Type Functional Equation [PDF]
Journal of Applied Analysis, 2007 Suppose that \(M\) is a Abelian group in which the unique division by 2 and 3 is performable and \(S\) is an abstract cone satisfying the cancellation law. In this paper the author proves that if \(f:M\to S\) is a solution of the Jensen functional equation, then it is a solution of the following equation \[ 3(b-1) f\biggl(\frac{x+y+z}{3}\biggr)+ f(x)+f(
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On Jensen’s and the quadratic functional equations with involutions [PDF]
Proyecciones (Antofagasta), 2017 We determine the Solutions f : S → H of the generalized Jensen’s functional equation f( x + σ(y)) + f( x + τ(y)) = 2f(x), x , y∈ Sand the solutions f : S → H of the generalized quadratic functional equationf ( x + σ(y)) + f (x + τ(y)) = 2f (x) + 2f (y), x, y ∈ S,where S is a commutative semigroup, H is an abelian group (2-torsion free in the first ...
Fadli, B. +3 more
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Jensen’s and the quadratic functional equations with an endomorphism [PDF]
Proyecciones (Antofagasta), 2017 We determine the solutions f : S → H of the generalized Jensen’s functional equation f (x + y) + f (x + φ(y)) = 2f (x), x,y ∈ S,and the solutions f : S → H of the generalized quadratic functional equation f (x + y) + f (x + φ(y)) = 2f (x) + 2f (y), x,y ∈ S,where S is a commutative semigroup, H is an abelian group (2-torsion free in the first ...
Sabour, KH, Kabbaj, S
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On Jensen's functional equation
Aequationes Mathematicae, 1992 The following is offered as main result. Let \((G,\cdot)\) and \((H,+)\) be abelian groups, and \(e\) the neutral element of \((G,\cdot)\). The solutions \(f: G\to H\) of \(f(xy)+f(xy^{-1})=2f(x)\), \(f(e)=0\) are exactly the homomorphisms of \(G\to H\) if, and only if, either \(H\) has no element of order 2 or \([G:G^ 2]\leq 2\), where \(G^ 2:=\{x^ 2 ...
Vasudeva, H.L., Parnami, J.C.
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Functional Differential Equations and Jensen’s Inequality [PDF]
Journal of Mathematical Analysis and Applications, 1987 The authors study various types of stability of the functional differential equations \(x'(t)=F(t,x_ t)\) where \(x_ t(s)=x(t+s),\)- h\(\leq s\leq 0\), and h is a positive constant. The main tool is the Lyapunov functionals. These functionals satisfy certain conditions involving functions which verify Jensen's inequality.
Becker, Leigh C +2 more
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On the stability of generalized d′Alembert and Jensen functional equations [PDF]
International Journal of Mathematics and Mathematical Sciences, 2006 The aim of this paper is to study the stability problem of the generalized d′Alembert, Wilson, and Jensen functional equations.
Kyung Hui Kim, Sever Silvestru Dragomir
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