Research On The Related Problems Of The Integral Means Of Analytic Functions

In this paper,we investigate the convexities and logarithmic convexities of Gaussian integral means Mp,⒑(f,r),the weighted integral means Aα,β(f,r)andLα,β(f,r)and area integral means Mp,α,β,c(f,r)of analytic functions.The main contents of the paper are as follows.In chapter one,the research background and present situation of the integral means of analytic functions are introduced,and we provide some basic concepts to be used in this paper.In chapter two,we investigate the logarithmic convexities of Gaussian integral means Mp,α(f,r)with respect to In r,where f(z)=z3+a.In chapter three,the logarithmic convexities of the weighted integral means Aα,β(f,r)of the mixed area of f(rD)and the weighted integral means Lα,β(f,r)of the mixed length of(?)f(rD)with respect to r are explored,where ∈{0,1,2}.In chapter four,under the weighted area measure |z|2β(1-|z|2)αdA(z),the logarithmic convexities of the area integral means Mp,α,β,c(f,r)with respect to r on c ≤|z|≤r are discussed.