Journal ArticleDOI
Mean value in invexity analysis
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In this article, a generalization of the mean value theorem is considered in the case of functions defined on an invex set with respect to η (which is not necessarily connected).Abstract:
In this paper, a generalization of the mean value theorem is considered in the case of functions defined on an invex set with respect to η (which is not necessarily connected).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.
Journal ArticleDOI
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
Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex
TL;DR: In this article, the Hermite-Hadamard-type inequality for preinvex functions is extended to functions of several variables on invex subsets of a function.
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.
Journal Article
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.
References
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Book
Optimization and nonsmooth analysis
TL;DR: The Calculus of Variations as discussed by the authors is a generalization of the calculus of variations, which is used in many aspects of analysis, such as generalized gradient descent and optimal control.
Book
Principles of mathematical analysis
TL;DR: The real and complex number system as discussed by the authors is a real number system where the real number is defined by a real function and the complex number is represented by a complex field of functions.
Book
Nonlinear Programming: Theory and Algorithms
TL;DR: The book is a solid reference for professionals as well as a useful text for students in the fields of operations research, management science, industrial engineering, applied mathematics, and also in engineering disciplines that deal with analytical optimization techniques.
Book
Nonlinear Programming
TL;DR: It is shown that if A is closed for all k → x x, k → y y, where ( k A ∈ ) k y x , then ( ) A ∉ y x .