منابع مشابه
On Properties of Geodesic η-Preinvex Functions
The present paper deals with the properties of geodesic η-preinvex functions and their relationships with η-invex functions and strictly geodesic η-preinvex functions. The geodesic η-pre-pseudo-invex and geodesic η-pre-quasi-invex functions on the geodesic invex set are introduced and some of their properties are discussed.
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In this paper, we define and introduce some new concepts of strongly φ-preinvex (φ-invex) functions and strongly φη-monotone operators. We establish some new relationships among various concepts of φ-preinvex (φ-invex) functions. As special cases, one can obtain various new and known results from our results. Results obtained in this paper can be viewed as refinement and improvement of previous...
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Convexity and generalized convexity play a central role in mathematical economics, engineering, and optimization theory. Therefore, the research on convexity and generalized convexity is one of the most important aspects in mathematical programming (see [1–4, 6–11] and the references therein). Weir and Mond [7] and Weir and Jeyakumar [6] introduced the definition of preinvexity for the scalar f...
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and Applied Analysis 3 Example 2.3. Let X be a subset in Rn defined as follows: X : { x1, x2 | 0 < x2 < x2 1, 0 < x1 < 2 } ∪ { 0, 0 }. 2.2 Consider the point u 0, 0 . Since the tangent line of the curve x2 x2 1 at point u is the line x2 0. Then, for any x ∈ X \ {u}, there exists 0 < λ0 < 1 such that u λη x, u / ∈ X, ∀λ ∈ 0, λ0 . 2.3 Therefore, there exists no vector-valued function η x, u / 0 s...
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*Correspondence: [email protected] 1Department of Mathematics, Hanshan Normal University, Chaozhou, Guangdong 521041, China Full list of author information is available at the end of the article Abstract With the equivalent relationships between the G-generalized invexities and general invexities on the hand, we present two characterizations for G-preinvexity; we also discuss the relationships...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2001
ISSN: 0022-247X
DOI: 10.1006/jmaa.2000.7310