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A function $f : I \to ℝ$ , where $I \subseteq ℝ$ is an interval, is said to be a convex function on $I$ if $f (t x + (1 - t) y) \leq t f (x) + (1 - t) f (y)$ holds for all $x, y \in I$ and $t \in [0, 1]$ . There are several papers in the literature which discuss properties of convexity and contain integral inequalities. Furthermore, new classes of convex functions have been introduced in order to generalize the results and to obtain new estimations. We define some new classes of convex functions that we name quasi-convex, Jensen-convex, Wright-convex, Jensen-quasi-convex and Wright-quasi-convex functions...

On $D$ -preinvex-type functions.

Peng, Jian-Wen, Zhu, Dao-Li (2006)

Journal of Inequalities and Applications [electronic only]

On generalized derivatives for $C^{1, 1}$ vector optimization problems.

La Torre, Davide (2003)

Journal of Applied Mathematics

On generalized preinvex functions and monotonicities.

Noor, Muhammad Aslam (2004)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

On Hadamard's inequality on a disk.

Dragomir, S.S. (2000)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

On jensen type inequalities with ordered variables.

Cirtoaje, Vasile (2008)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

On Locally Subadditive Functions

Slavko Simić, Stojan Radenović (1994)

Matematički Vesnik

On midpoint convex set-valued functions.

Kazimierz Nikodem (1987)

Aequationes mathematicae

On new inequalities of Hadamard-type for Lipschitzian mappings and their applications.

Wang, Liang-Cheng (2007)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

On relations among the generalized second-order directional derivatives

Karel Pastor (2001)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In the paper, we deal with the relations among several generalized second-order directional derivatives. The results partially solve the problem which of the second-order optimality conditions is more useful.

On Schur convexity of some symmetric functions.

Xia, Wei-Feng, Chu, Yu-Ming (2010)

Journal of Inequalities and Applications [electronic only]

On semiconvexity properties of rotationally invariant functions in two dimensions

Miroslav Šilhavý (2004)

Czechoslovak Mathematical Journal

Let $f$ be a function defined on the set $𝐌^{2 \times 2}$ of all $2$ by $2$ matrices that is invariant with respect to left and right multiplications of its argument by proper orthogonal matrices. The function $f$ can be represented as a function $\tilde{f}$ of the signed singular values of its matrix argument. The paper expresses the ordinary convexity, polyconvexity, and rank 1 convexity of $f$ in terms of its representation $\tilde{f} .$

Currently displaying 1 – 20 of 31

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Displaying 1 – 20 of 31

On a Class of Nonconvex Problems Where all Local Minima are Global

On a new class of refined discrete Hardy-type inequalities.

On an inequality of V. Csiszár and T.F. Móri for concave functions of two variables.

On an upper bound for Jensen's inequality.

On Contractibility of the Operator i-t Nabla f

On co-ordinated quasi-convex functions

On $D$ -preinvex-type functions.

On generalized derivatives for $C^{1, 1}$ vector optimization problems.

On generalized preinvex functions and monotonicities.

On Hadamard's inequality on a disk.

On jensen type inequalities with ordered variables.

On Locally Subadditive Functions

On midpoint convex set-valued functions.

On new inequalities of Hadamard-type for Lipschitzian mappings and their applications.

On relations among the generalized second-order directional derivatives

On Schur convexity of some symmetric functions.

On semiconvexity properties of rotationally invariant functions in two dimensions

On strongly generalized preinvex functions.

On the abstract Hahn-Banach theorem due to Rodé.

On the composition of quasiconvex functions and the transposition.

Currently displaying 1 – 20 of 31