Abstract:
On SomeClassesofGeneralized k-Uniformly Analytic
FunctionsandRelatedTopics
The mainfocusofthisstudyistode necertainnewclassesofanalyticfunctionsusingthe
concepts ofboundedboundaryrotationandboundedradiusrotationaswellassomeof
their generalizationsinconicdomains.Thisresearchmostlydependsonthetechniquesof
convolution(Hadamardproduct)anddi erentialsubordination.WeusetheRuscheweyh
derivative,theNoorintegraloperatorandthegeneralizedSalageanoperatortode nesome
new classesofanalyticfunctions.Somegeometricandanalyticpropertiessuchasinclusion
relations, integralpreservingpropertiesundercertainintegraloperators,radiusproblems,
rate ofgrowthproblems,closureunderconvolutionwithconvexfunctions,Hankeldeter-
minantproblemandFekete-Szegotypeinequalitiesareinspectedsystematically.Mostof
the resultsaresharp.Wealsodiscusstheconnectionsoftheseresultswithalreadyexisting
classes inthepreviousliteratureofthesubject.Thisresearchisrationalizedwiththe
advancedtrendsinthe eldofGeometricFunctionTheory.
