Applications of Some Subclasses of Meromorphic Functions Associated with the q-Derivatives of the q-Binomials
Ekram E. Ali, H. M. Srivastava, A. Y. Lashin, Abeer M. Albalahi
Abstract
In this article, we make use of the q-binomial theorem to introduce and study two new subclasses ℵ(αq,q) and ℵ(α,q) of meromorphic functions in the open unit disk U, that is, analytic functions in the punctured unit disk U∗=U\{0}={z:z∈Cand0<z<1}. We derive inclusion relations and investigate an integral operator that preserves functions which belong to these function classes. In addition, we establish a strict inequality involving a certain linear convolution operator which we introduce in this article. Several special cases and corollaries of our main results are also considered.
Topics & Concepts
Meromorphic functionUnit diskMathematicsConvolution (computer science)Analytic functionOperator (biology)Binomial (polynomial)Pure mathematicsUnit (ring theory)Discrete mathematicsFunction (biology)Algebra over a fieldComputer scienceChemistryTranscription factorBiologyRepressorMachine learningStatisticsArtificial neural networkBiochemistryGeneMathematics educationEvolutionary biologyAnalytic and geometric function theoryMeromorphic and Entire FunctionsHolomorphic and Operator Theory