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A Class of Analytic Starlike Functions Associated with Petal Like Region on the Positive Half of Complex Plane


Affiliations
1 Department of Mathematics, Govt. Post Graduate College, Gopeshwar, Chamoli Uttarakhand - 246401, India
2 Department of Mathematics and Astronomy, Lucknow University Lucknow - 222207, India
     

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In the light of Riemann open mapping theorem, if we map open unit disk U conformally onto a region then depending on the geometry of boundary of we can always extract a subclass of H[a, n] by subordinating various functionals of the function f ∈ H[a, n]. Depending upon the geometry of the range set attempts have been made to find some algebraic structure in such classes, for that Hankel determinant of coefficients of functions pertaining to these classes have been studied, bounds of various coefficients have been determined and also based on the subordination principle we have determined radius |z| < r ;z ∈ U for which f belongs to such a class. In this paper our focus would be on n−PS* defined as n − PS* = {f ∈ A : Re {zf'(z)/f(z)} > 0,|(zf'(z)/f(z))n - 1|<1}.

Keywords

Strongly Starlike Functions, Petal Like Region, Subordination, Hankel Determinant.
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  • A Class of Analytic Starlike Functions Associated with Petal Like Region on the Positive Half of Complex Plane

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Authors

Rajesh Kumar Maurya
Department of Mathematics, Govt. Post Graduate College, Gopeshwar, Chamoli Uttarakhand - 246401, India
Poonam Sharma
Department of Mathematics and Astronomy, Lucknow University Lucknow - 222207, India

Abstract


In the light of Riemann open mapping theorem, if we map open unit disk U conformally onto a region then depending on the geometry of boundary of we can always extract a subclass of H[a, n] by subordinating various functionals of the function f ∈ H[a, n]. Depending upon the geometry of the range set attempts have been made to find some algebraic structure in such classes, for that Hankel determinant of coefficients of functions pertaining to these classes have been studied, bounds of various coefficients have been determined and also based on the subordination principle we have determined radius |z| < r ;z ∈ U for which f belongs to such a class. In this paper our focus would be on n−PS* defined as n − PS* = {f ∈ A : Re {zf'(z)/f(z)} > 0,|(zf'(z)/f(z))n - 1|<1}.

Keywords


Strongly Starlike Functions, Petal Like Region, Subordination, Hankel Determinant.

References





DOI: https://doi.org/10.18311/jims%2F2020%2F25449