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.

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)

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)

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.

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)

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.

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].

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]).

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.