Abstract
Making use of the linear operator defined in (Prajapat, 2012), we introduce the class of analytic and -valent functions in the open unit disk . Furthermore, we obtain some sufficient conditions for starlikeness and close-to-convexity and some angular properties for functions belonging to this class. Several corollaries and consequences of the main results are also considered.
Highlights
Making use of the linear operator JJmppm(λλλ λλλ de ned in (Pra apat, 2012), we introduce the class BBmppm(λλλ λλλ λλλ λλλ of analytic and pp-valent functions in the open unit disk UU
We obtain some sufficient conditions for starlikeness and close-to-convexity and some angular properties for functions belonging to this class
Let AApp(nnn denote the class of functions ffffff of the form ff(zz) = zzpp + aakkzzkk, ppppp p p pp {1, 2, 3, ...}, (1)
Summary
Making use of the linear operator JJmppm(λλλ λλλ de ned in (Pra apat, 2012), we introduce the class BBmppm(λλλ λλλ λλλ λλλ of analytic and pp-valent functions in the open unit disk UU. Let AApp(nnn denote the class of functions ffffff of the form ff(zz) = zzpp + aakkzzkk, ppppp p p pp {1, 2, 3, ...} , (1) A function fffffffffpp(nnn is said to be in the class CCpp(nnnnnn of pp-valently close-to-convex of order αα in UU if and only if it satis es the inequality ff′(zz) zzpppp JJmppm (λλλ λλ) pp p pp p pp ppppp p pp p ppp mm
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