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By The Linear Operator Defined In A Class Of P-analytic Functions,

Posted on:2007-01-03Degree:MasterType:Thesis
Country:ChinaCandidate:Y WeiFull Text:PDF
GTID:2190360185461056Subject:Basic mathematics
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Since defined Ruscheweyh derivatives of analytic functions by S. Ruscheweyh[1], many scholars have studied classes of univalent or multivalent analytic functions associated with Ruscheweyh derivatives( [2],[3],[4] ).Recently, based on different linear operators,some properties and characters of p -valent analytic functions and meromorphic multivalent functions have been investigated extensively( [5],[6],[7] ).In this article,let Ap be the class of functions analytic in the open unit disk U .For n is any integer greater than -p,a certain linear operator In+p:Ap→Ap is defined as In+pf(Z)=fp-1(Z)*f(Z)such that fp-1(Z)*fp(Z)=sp/(1-z)n+p where fp(Z)=sp/(1-Z)p and * denotes convolution or Hadamard product.Firstly,making use of operator In+p,subclass Sn+p*(η;A,B) is introduced in the open unit disk,the inclusion relation of Sn+p+1*(η;A,B)?Sn+p*(η;A,B) and the best dominant function of differential subordination q1(Z) are obtained,furthermore,some conclusions are acquired according to the special parameters A and B .Some properties of class Sn+p*(η;A,B) are preserved in connection with the operator Fλ,p and the best dominant function q2(Z) can aslo be obtained.Secondly,class Tn+p(η;A,B) of analytic functions belonging to Sn+p*(η;A,B) with the negative coefficients is investigated,the necessary and sufficient condition of f(Z) falling into Tn+p(η;A,B) is obtained,some relationships are preserved under the integral operator Fλ,p,the radius of starlike functions and convex functions are aslo considered.Finally,problems involving generalized neighborhoods and partial sums of analytic functions in class Ap are investigated,using fractional calculus operators of order u ,we...
Keywords/Search Tags:p -valent analytic functions, linear operator, best dominant, starlike functions, convex functions, neighborhoods of analytic functions, partial sums, fractional calculus operators
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