Chiang Mai Journal of Science

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New classes of  complex-valued, multivalent harmonic functions of  the form f = h + g , where  h and  g  are multivalent analytic in the unit disk are introduced. We give sufficient conditions for these classes. These coefficient conditions are shown to be also necessary if  the coefficients of   h  and  g  of  the harmonic functions  f = h + g are negative. Furthermore, we determine a representation theorem, extreme points, distortion and covering theorems, convolution conditions and convex combinations for these functions.

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