CERTAIN BOUNDS FOR UNIFIED CONVEX FUNCTIONS OF $q$-DIFFERENCE OPERATOR

ON CONVEX OPERATOR FOR (p, q)-ANALYTIC FUNCTIONS

We recall here some of the definitions given in [7]. Definition 1. The ’discrete plane’ Q′ with respect to some fixed point z′ = (x′, y′) in the first quadrant, is defined by the set of lattice points, Q′ = {(pmx′, qny′) : m,n ∈ Z the set of integers}. Definition 2. Two lattice points zi, zi+1 ∈ Q′ are said to be ’adjacent’ if zi+1 is one of (pxi, yi), (p−1xi, yi), (xi, qyi) or (xi, q−1yi). Def...

Properties of multivalent functions associated with certain integral operator

Let A(p) denote the class of functions which are analytic in the open unit disk U. By making use of certain integral operator,we obtain some interesting properties of multivalent analytic functions.

Certain Inequalities for Convex Functions

This is a review paper on some new inequalities for convex functions of one and several variables. The most important result presented for convex functions of one variable is the extension of Jensen’s inequality to affine combinations. The most interesting results presented for convex functions of several variables refer to inequalities concerning simplexes and its cones. Mathematics subject cl...

Certain Convex Harmonic Functions

Some properties and results for certain subclasses of starlike and convex functions

In the present paper, we introduce and investigate some properties of two subclasses $ Lambda_{n}( lambda , beta ) $ and $ Lambda_{n}^{+}( lambda , beta ) $;  meromorphic and starlike  functions of order $ beta $. In particular, several inclusion relations, coefficient estimates, distortion theorems and covering theorems are proven here for each of these function classes.