On Some Classes of Generalized k-Uniformly Analytic Functions and Related Topics

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.