Open AccessНекоторые результаты о подчинении для одного функционального класса, определяемого $q$-разностным оператором типа Салагина
Author(s) -
M.K. Aouf,
T.M. Seoudy
Publication year - 2020
Publication title -
vladikavkazskij matematičeskij žurnal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.126
H-Index - 2
eISSN - 1814-0807
pISSN - 1683-3414
DOI - 10.46698/q5183-3412-9769-d
Subject(s) - subordination (linguistics) , operator (biology) , calculus (dental) , mathematics , analytic function , type (biology) , pure mathematics , order (exchange) , algebra over a field , unit disk , discrete mathematics , medicine , ecology , philosophy , linguistics , biochemistry , chemistry , dentistry , finance , repressor , biology , transcription factor , economics , gene
The theory of the basic quantum calculus (that is, the basic q-calculus) plays important roles in many diverse areas of the engineering, physical and mathematical science. Making use of the basic definitions and concept details of the q-calculus, Govindaraj and Sivasubramanian [10] defined the Salagean type q-difference (q-derivative) operator. In this paper, we introduce a certain subclass of analytic functions with complex order in the open unit disk by applying the Salagean type q-derivative operator in conjunction with the familiar principle of subordination between analytic functions. Also, we derive some geometric properties such as sufficient condition and several subordination results for functions belonging to this subclass. The results presented here would provide extensions of those given in earlier works.