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). Definition 3. A ’ discrete curve’ C in Q′ connecting z0 to zn is denoted by the sequence C ≡ 〈z0, z1, . . . , zn〉, where zi, zi+1; i = 0, 1, . . . , (n− 1) are adjacent points of Q′. If the points are distinct (zi 6= zj ; i 6= j) then the discrete curve C is said to be ’simple’.