A note onG-preinvex functions
نویسندگان
چکیده
*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 between different G-generalized invexities such as G-preinvexity, strict G-preinvexity and semistrict G-preinvexity. Note that our results are proved by applying the results from general invexities introduced in the literatures.
منابع مشابه
New integral inequalities for $s$-preinvex functions
In this note, we give some estimate of the generalized quadrature formula of Gauss-Jacobi$$underset{a}{overset{a+eta left( b,aright) }{int }}left( x-aright)^{p}left( a+eta left( b,aright) -xright) ^{q}fleft( xright) dx$$in the cases where $f$ and $left| fright| ^{lambda }$ for $lambda >1$, are $s$-preinvex functions in the second sense.
متن کاملOn Hadamard Integral Inequalities Involving Two Log-preinvex Functions
In this paper, we establish some new Hermite-Hadamard type integral inequalities involving two log-preinvex functions. Note that log-preinvex functions are nonconvex functions and include the log-convex functions as special cases. As special cases, we obtain the well known results for the convex functions.
متن کاملSome Integral Inequalities of Hermite-Hadamard Type for Multiplicatively s-Preinvex Functions
In this paper, we establish integral inequalities of Hermite-Hadamard type for multiplicativelys-preinvex functions. We also obtain some new inequalities involving multiplicative integralsby using some properties of multiplicatively s-preinvex and preinvex functions.
متن کاملOstrowski type inequalities for functions whose derivatives are preinvex
In this paper, making use of a new identity, we establish new inequalities of Ostrowski type for the class of preinvex functions and gave some midpoint type inequalities.
متن کاملOn Semi- B,G -Preinvex Functions
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...
متن کامل