Multivalent Functions and Differential Operator Extended by the Quantum Calculus
Samir Hadid, Rabha W. Ibrahim, Shaher Momani
Abstract
We used the concept of quantum calculus (Jackson’s calculus) in a recent note to develop an extended class of multivalent functions on the open unit disk. Convexity and star-likeness properties are obtained by establishing conditions for this class. The most common inequalities of the proposed functions are geometrically investigated. Our approach was influenced by the theory of differential subordination. As a result, we called attention to a few well-known corollaries of our main conclusions.
Topics & Concepts
Differential calculusConvexityCalculus (dental)Subordination (linguistics)Class (philosophy)Time-scale calculusOperator (biology)MathematicsDifferential (mechanical device)Unit diskDifferential operatorPure mathematicsAlgebra over a fieldMultivariable calculusComputer sciencePhysicsEngineeringDentistryChemistryBiochemistryGeneMedicineEconomicsPhilosophyThermodynamicsArtificial intelligenceFinancial economicsLinguisticsTranscription factorControl engineeringRepressorAnalytic and geometric function theoryPolymer Synthesis and Characterization