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In this paper, the sharp solutions of Fekete-Szegö problems are provided for class of quasi-convex mappings  f  1  of type B and class of quasi-convex mappings  f  2  of type B and order  α  defined on the unit ball in a complex Banach space, respectively, where  x  = 0 is a zero of order  k  + 1 of  f i  ( x ) −  x  ( i  = 1, 2). Compare with some recent works, our main theorems hold without additional restrictive conditions. Also, the proof of our main theorems are more simple than those given in the previous results.

Coefficient Problems of Quasi-Convex Mappings of Type B on the Unit Ball in Complex Banach Spaces