Abstract In the present investigation, we introduce and study interesting properties of a new unified class of pre-starlike functions with negative coefficients in the open unit disk ∆. These properties include growth and distortion, radii of convexity, radii of starlikeness and radii of close to convexity. 2000 Mathematics Subject Classification: 30C45.

If F is a vector space over an ordered division ring, C a convex subset of V and L the lattice of convex subsets of C, then we call L a convexity lattice. We give necessary and sufficient conditions for an abstract lattice to be a convexity lattice in the finite dimensional case.

Abstract. By making use of the generalized hypergeometric functions, in this paper we introduce and investigate certain new subclasses of analytic functions of complex order defined in the open unit disk. Coefficient inequalities, radii of close-to-convexity, starlikeness and convexity, closure theorems, integral means inequalities and several relations associated with (n, δ)-neighborhood for t...

We study conjugate and Lagrange dualities for composite optimization problems within the framework of abstract convexity. provide conditions zero duality gap in duality. For duality, intersection property is applied to obtain gap. Connection between dual also established. Examples related convex weakly functions are given.

We consider two different notions of convexity of metric spaces, namely (strict/uniform) ball convexity and (strict/uniform) distance convexity. Our main theorem states that (strict/uniform) distance convexity is preserved under a fairly general product construction, whereas we provide an example which shows that the same does not hold for (strict/uniform) ball convexity, not even when consider...