# On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions

Fractional Calculus and Applied Analysis (2006)

- Volume: 9, Issue: 2, page 159-176
- ISSN: 1311-0454

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topKiryakova, Virginia. "On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions." Fractional Calculus and Applied Analysis 9.2 (2006): 159-176. <http://eudml.org/doc/11266>.

@article{Kiryakova2006,

abstract = {2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35Recently, many papers in the theory of univalent functions have been
devoted to mapping and characterization properties of various linear integral
or integro-differential operators in the class S (of normalized analytic and
univalent functions in the open unit disk U), and in its subclasses (as the
classes S∗ of the starlike functions and K of the convex functions in U).
Among these operators, two operators introduced by Saigo, one involving
the Gauss hypergeometric function, and the other - the Appell (or Horn)
F3-function, are rather popular. Here we view on these Saigo’s operators
as cases of generalized fractional integration operators, and show that the
techniques of the generalized fractional calculus and special functions are
helpful to obtain explicit sufficient conditions that guarantee mappings as:
S → S and K → S, that is, preserving the univalency of functions.* Partially supported by National Science Fund (Bulg. Ministry of Educ. and Sci.) under Project MM 1305.},

author = {Kiryakova, Virginia},

journal = {Fractional Calculus and Applied Analysis},

keywords = {26A33; 30C45; 33A35},

language = {eng},

number = {2},

pages = {159-176},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions},

url = {http://eudml.org/doc/11266},

volume = {9},

year = {2006},

}

TY - JOUR

AU - Kiryakova, Virginia

TI - On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions

JO - Fractional Calculus and Applied Analysis

PY - 2006

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 9

IS - 2

SP - 159

EP - 176

AB - 2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35Recently, many papers in the theory of univalent functions have been
devoted to mapping and characterization properties of various linear integral
or integro-differential operators in the class S (of normalized analytic and
univalent functions in the open unit disk U), and in its subclasses (as the
classes S∗ of the starlike functions and K of the convex functions in U).
Among these operators, two operators introduced by Saigo, one involving
the Gauss hypergeometric function, and the other - the Appell (or Horn)
F3-function, are rather popular. Here we view on these Saigo’s operators
as cases of generalized fractional integration operators, and show that the
techniques of the generalized fractional calculus and special functions are
helpful to obtain explicit sufficient conditions that guarantee mappings as:
S → S and K → S, that is, preserving the univalency of functions.* Partially supported by National Science Fund (Bulg. Ministry of Educ. and Sci.) under Project MM 1305.

LA - eng

KW - 26A33; 30C45; 33A35

UR - http://eudml.org/doc/11266

ER -

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