In this paper, new Hermite-Hadamard type inequalities for coordinated convex and co-ordinated quasi convex functions are proved in a unique way. These results generalize many results proved in earlier works for these classes of functions. Finally, applications of our results are given to estimate the product of moments of two independent continuous random variables.

In this manuscript, we introduce concepts of (m1,m2)-logarithmically convex (AG-convex) functions and establish some Hermite-Hadamard type inequalities of these classes of functions.

We introduce a wide subclass F(X,ω) of quasi-plurisubharmonic functions in a compact Kähler manifold, on which the complex Monge-Ampère operator is well-defined and the convergence theorem is valid. We also prove that F(X,ω) is a convex cone and includes all quasi-plurisubharmonic functions which are in the Cegrell class.

In this paper, a new weighted identity for differentiable functions of two variables defined on a rectangle from the plane is established. By using the obtained identity and analysis, some new weighted integral inequalities for the classes of co-ordinated convex, co-ordinated wright-convex and co-ordinated quasi-convex functions on the rectangle from the plane are established which provide weig...

In this paper we introduce new subclasses of p-valent starlike, pvalent convex, p-valent close-to-convex and p-valent quasi-convex meromorphic functions and investigate some inclusion properties of these subclasses and investigate various inclusion properties and integral-preserving properties for the p-valent meromorphic function classes.

In 1976, P. R. Scott characterized the Ehrhart polynomials of convex integral polygons. We study the same question for Ehrhart polynomials and quasi-polynomials of nonintegral convex polygons. Define a pseudo-integral polygon, or PIP, to be a convex rational polygon whose Ehrhart quasipolynomial is a polynomial. The numbers of lattice points on the interior and on the boundary of a PIP determin...

We construct a quasi-Banach space which cannot be given an equivalent plurisubharmonic quasi-norm, but such that it has a quotient by a onedimensional space which is a Banach space. We then use this example to construct a compact convex set in a quasi-Banach space which cannot be atfinely embedded into the space L0 of all measurable functions.

in this paper, we study the convexity of the integral operator

Let F be an arbitrary topological vector space; we shall say that a subset S of F is quasi-convex if the set of continuous affine functionals on 5 separates the points of S. If X is a Banach space and T: X -* F is a continuous linear operator, then T is quasi-convex if T(U) is quasiconvex, where U is the unit ball of X. In the case when T is compact, T(U) is quasi-convex if and only if it is af...