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Generalized invexity and generalized invariant monotonicity
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In this article, several kinds of invariant monotone maps and generalized invariant maps are introduced, and relations between generalized monotonicity and generalized invexity are established, which are generalizations of those presented by Karamardian and Schaible.Abstract:
In this paper, several kinds of invariant monotone maps and generalized invariant monotone maps are introduced. Some examples are given which show that invariant monotonicity and generalized invariant monotonicity are proper generalizations of monotonicity and generalized monotonicity. Relationships between generalized invariant monotonicity and generalized invexity are established. Our results are generalizations of those presented by Karamardian and Schaible.read more
Citations
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Journal ArticleDOI
Some quantum integral inequalities via preinvex functions
TL;DR: Some new quantum analogues of Hermite-Hadamard and Iyengar type inequalities for some classes of preinvex functions are obtained.
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Properties and integral inequalities of Hadamard- Simpson type for the generalized (s,m) -preinvex functions
TL;DR: In this paper, the power of the absolute of the first derivative is defined as a generalized (s,m)-preinvex function, and a Hadamard-Simpson type integral inequality is established for a function of which the power is generalized.
Journal ArticleDOI
On hermite-hadamard inequalities for h-preinvex functions
TL;DR: In this paper, the Hermite-Hadamard type inequalities for h-preinvex functions are established under certain conditions, which can be viewed as generalization of several previously known results.
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Hermite-Hadamard inequality for functions whose derivative absolute value are P−convex
A. Barani,Saeed Barani +1 more
TL;DR: In this paper, the right hand side of a Hermite-Hadamard type inequality for functions whose derivatives absolute values are P−convex was extended to the case of functions whose absolute values can be expressed by trapezoidal formulas and special means.
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On Hadamard integral inequalities involving two log-preinvex functions.
TL;DR: In this paper, the Hermite-Hadamard type integral inequalities involving two log-preinvex functions are established for nonconvex and convex functions, respectively.
References
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On sufficiency of the Kuhn-Tucker conditions
Morgan A Hanson,Morgan A Hanson +1 more
TL;DR: In this paper, it was shown that there are other wide classes of functions for which the pseudo-convexity of&(x) and quasiconvexeness off(x)-conditions are sufficient for optimality.
Journal ArticleDOI
Pre-invex functions in multiple objective optimization
T. Weir,Bertram Mond +1 more
TL;DR: In this paper, a saddlepoint optimality condition for convex-like programs was given for differentiable functions f: S + R for which there exists an n-dimensional vector function q(,q U) such that for all x, u, u E S, q U is a convex function.
Journal ArticleDOI
On Invex Sets and Preinvex Functions
S. R. Mohan,S. K. Neogy +1 more
TL;DR: In this paper, the authors consider the class of the invex functions introduced by Hanson and show that under certain conditions, a function defined on a set of non-invex sets A is pre-quasi-inverse on A.
Journal ArticleDOI
Seven kinds of monotone maps
S. Karamardian,S. Schaible +1 more
TL;DR: In this article, pure first-order characterizations of various types of generalized convex functions are obtained for gradient maps and generalized monotonicity properties of the underlying function are related to the convexity properties of gradient maps.
Journal ArticleDOI
Invexity and generalized convexity
TL;DR: In this paper, the relationship between invexity and generalized convexity was investigated, and necessary and sufficient conditions for a differentiable function to be η-invex were given, which are natural extensions of the analogous conditions for convex functions.