Let H denote the class of complex-valued harmonic functions f defined in the open unit disc D and normalized by f(0)=fz(0)-1=0.In this paper,we define a new generalized subclass of H associated with the(p,q)-Ruschewey...Let H denote the class of complex-valued harmonic functions f defined in the open unit disc D and normalized by f(0)=fz(0)-1=0.In this paper,we define a new generalized subclass of H associated with the(p,q)-Ruscheweyh-type harmonic differential operator in D.We first obtain a sufficient coefficient condition that guarantees that a function f in H is sense-preserving harmonic univalent in D and belongs to the aforementioned class.Using this coefficient condition,we then examine ratios of partial sums of f in H.In all cases the results are sharp.In addition,the results so obtained generalize the related works of some authors,and many other new results are obtained.展开更多
文摘Let H denote the class of complex-valued harmonic functions f defined in the open unit disc D and normalized by f(0)=fz(0)-1=0.In this paper,we define a new generalized subclass of H associated with the(p,q)-Ruscheweyh-type harmonic differential operator in D.We first obtain a sufficient coefficient condition that guarantees that a function f in H is sense-preserving harmonic univalent in D and belongs to the aforementioned class.Using this coefficient condition,we then examine ratios of partial sums of f in H.In all cases the results are sharp.In addition,the results so obtained generalize the related works of some authors,and many other new results are obtained.
