Investigating New Subclasses of Bi-Univalent Functions Associated with q-Pascal Distribution Series Using the Subordination Principle
Abdullah Alsoboh, Ala Amourah, Maslina Darus, Carla Amoi Rudder
Abstract
In the real world, there are many applications that find the Pascal distribution to be a useful and relevant model. One of these is the normal distribution. In this work, we develop a new subclass of analytic bi-univalent functions by making use of the q-Pascal distribution series as a construction. These functions involve the q-Gegenbauer polynomials, and we use them to establish our new subclass. Moreover, we solve the Fekete–Szegö functional problem and analyze various different estimates of the Maclaurin coefficients for functions that belong to the new subclass.
Topics & Concepts
Pascal (unit)Subordination (linguistics)SubclassMathematicsAnalytic functionDistribution (mathematics)Pure mathematicsSeries (stratigraphy)Univalent functionApplied mathematicsComputer scienceMathematical analysisImmunologyAntibodyLinguisticsProgramming languagePhilosophyBiologyPaleontologyAnalytic and geometric function theoryMathematical functions and polynomialsAdvanced Mathematical Identities