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Search Results: 1 - 10 of 28013 matches for " Semistrictly B-preinvex function "
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Strictly B -Preinvex Functions
严格 B -预不变凸函数

Peng Jianwen,Zhu Daoli,

数学物理学报(A辑) , 2006,
Abstract: In this paper, a sufficient condition of the strictly B-preinvex function is firstly obtained. Then some properties of the strictly B-preinvex function are shown. Finally, some results for the minimization problem which the objective function is strictly B-preinvex are presented.
On Characterizing Solution Sets of Nonsmooth B-Preinvex Optimization Problems
WAN Xuan,ZHAO Ke-quan
Journal of Chongqing Normal University , 2012,
Abstract: In this paper, various characterizations of optimal solution sets of nonsmooth B-preinvex optimization problems with inequality constrains are given. Firstly, making use of Clarke’s subdifferential, we establish the optimality condition for this kind of optimization problem; secondly, we presented a property about the solution set S of constrained B-preinvex optimization proble; finally, five equivalent characterizations of the solution set are obtained, that is,* An example is given to illustrate that five solution sets are equal, i.e. S={0}.(* Indicates a formula, please see the full text)
Strongly G-Preinvex Functions
PENG Zai-yun,FANG Xiao-liang,ZHAO Yong
Journal of Chongqing Normal University , 2011,
Abstract: The paper gives a class fo new generalized convex function-strongly G-preinvex functions, it is a true generalization of strong preinvex function. First, three, examples have been got to show that it's existence, and strongly G-preinvex function is different from G-preinvex function and strictly G-preinvex function. Then, we discuses three properties of strongly G-preinvex function. Finally, we give a sufficient condition about strongly G-preinvex function under the case that G-preinvex function,namely, Let the set * is invex set with * is satisfied with condition * is a G-preinvex function. if * have * . Then, * is a strongly G-preinvex function on K with respect to *.(* Indicates a formula, please see the full text)
Optimality for Henig Proper Efficiency in Vector Optimization Involving Dini Set-Valued Directional Derivatives  [PDF]
Guolin Yu, Huaipeng Bai
Applied Mathematics (AM) , 2011, DOI: 10.4236/am.2011.27126
Abstract: This note studies the optimality conditions of vector optimization problems involving generalized convexity in locally convex spaces. Based upon the concept of Dini set-valued directional derivatives, the necessary and sufficient optimality conditions are established for Henig proper and strong minimal solutions respectively in generalized preinvex vector optimization problems.
A Characterization for r-Preinvex Function
ZHAO Ke-quan,LONG Pu-jun,WAN Xuan
Journal of Chongqing Normal University , 2011,
Abstract: In this paper, an equivalent condition for a clas of re-preinex function is etablished. A characterization for a twice continuously dierentiable r-preinvex function is obtained by the equivalent condition. Under ome suitable condition, the following result has been proved: Let * be open invex et with respect to * and * satisfy condition * defined on X is twice continuously dierentiable and satifies condition D. Then f is r-preinvex function with respect to * is and only if *. Our results improve and generalize some known result.(* Indicates a formula, please see the full text)
An Equivalent Condition of Preinvex Function
ZHAO Ke-quan
Journal of Chongqing Normal University , 2010,
Abstract: Generalized convexity has been playing an important role in mathematical programming . In this paper, an equivalent condition of twice continuously differentiable preinvex function is established by transforming multivariate real-valued function into univariate real-valued function. Suppose that X be open invex set with respect to η,ηsatisfies condition C , f be twice continuously differentiable and satisfies condition D. Then f is preinvex function with respect to η,ηsatisfies condition C, f be twice continuously differentible and satisfiles condition D. then f is preinvex function with respect to η if and only if νx,y∈X,η(x,y)tV2f(x)η(x,y)≥0. Our results provide new thoughts to verify the preinvexity of function and also generalize some known results.
Characteristics and Applications of Strongly G-preinvex Functions
PENG Zaiyun,ZHOU Xuanlin,ZHAO Yong
Journal of Chongqing Normal University , 2012,
An Equivalent Condition of r-preinvex Functions
Journal of Chongqing Normal University , 2009,
Abstract: An equivalent condition of r-preinvexity was given hy condition C which was introduced by S.R. Mohan and S.K. Neogy.In this paper another proof is provided about the equivalent condition by the use of the conclusion which upper semicontinuous function has maximum on compact set. That is, let K he an open invex set with respect to η and η satisfies condition C. Let f be a upper semicontinuous function that satisfies f(y+η(x,y))≤f(x),Ax,Y∈K. Then f is a r-preinvex function for the same ηif and only if Eα∈(0,1),Ax,y∈K,s.t.f(y+aη(x,y))≤log(αerf(x))+(1-α)erf(y))1/r,r≠0。f(y+aη(x,y))≤af(x)+(1-α)f(y)),r=0 The proof is absence of the assumption which set K is open and A is dense on [0,1].
On certain Bazilevi functions of order 2
Shigeyoshi Owa
International Journal of Mathematics and Mathematical Sciences , 1992, DOI: 10.1155/s0161171292000796
Abstract: A certain class B(n, ±, 2) of Bazilevi functions of order 2 in the unit disk is introduced. The object of the present paper is to derive some properties of functions belonging to the class B(n, ±, 2). Our result for the class B(n, ±, 2) is the improvement of the theorem by N. E. Cho ([1]).
Unsteady Incompressible Flow of a Generalised Oldroyed-B Fluid between Two Infinite Parallel Plates  [PDF]
D. Bose, U. Basu
World Journal of Mechanics (WJM) , 2013, DOI: 10.4236/wjm.2013.32012

This paper presents a study of visco-elastic flow of an incompressible generalized Oldroyd-B fluid between two infinite parallel plates in which the constitutive equation involves fractional order time derivative. The solutions of field equations are being obtained for the motion of the said fluid between two parallel plates where the lower plate starts to move with steady velocity and the upper plate remains fixed in the first problem and the upper plate oscillates with constant frequency and the other being at rest in the second problem. The exact solutions for the velocity field are obtained by using the Laplace transform and finite Fourier Sine transform technique in terms of Mittag Leffler and generalised functions. The analytical expression for the velocity fields are derived and the effect of fractional parameters upon the velocity field is depicted graphically.

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