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Title:	Properties of certain generalised subclasses of analytic functions generated by operators associated with quantum calculus
Authors:	Alsoboh Abdullah Mohammedkhalid Khalil (P92712)
Supervisor:	Maslina Darus, Prof. Dr.
Keywords:	Quantum calculus Universiti Kebangsaan Malaysia -- Dissertations Dissertations, Academic -- Malaysia
Issue Date:	31-Jan-2022
Description:	This research explores some generalised fractional integral, derivative and integral operators associated with quantum calculus (calculus without limits) on the space of normalised analytic functions in the open unit disk and meromorphic functions in the punctured unit disk. Some basic definitions and initial results of the geometric function theory used in this study are stated. These operators are defined by using the convolution technique and quantum calculus. In this current work, fractional q-integral operator and generalised derivative operator involving (p,q)-analogue of Ruscheweyh operator are constructed to define new classes of analytic and meromorphic functions. These classes are defined as associated with (p,q)-calculus. Some analytical and geometrical properties are studied, including coefficients inequalities, growth bounds, Distortion theorems, extreme points, and closures theorems. A new concept of q-neighborhoods, radii of q-starlikeness, and q-convexity are defined. Furthermore, the upper bounds for the Fekete-Szegö problem are solved with new subclasses defined by the concept of convolution associated with (p,q)-calculus. Additionally, new subclasses of analytic functions with respect to κ-symmetric points by replacing the right half-plane with a suitable domain are also introduced. The coefficient bounds, convolution properties and q-Jackson's integral representations for these subclasses are studied. Subsequently, new subclasses of meromorphic functions using a new differential operator involving the q-Ruscheweyh operator are introduced. In addition, some of the classical properties, including sufficient conditions, the upper and lower of its partial sums, and some results based on convolutions are derived. Finally, harmonic univalent functions and harmonic meromorphic functions are studied. New classes of harmonic functions defined by the new q-derivative operator are given and their properties are studied. The properties of the subclass of harmonic meromorphic starlike functions with respect to κ-symmetric points are investigated as well. The findings of this research are revised with the newfound methods and latest styles in geometric function theory.,Ph.D
Pages:	177
Publisher:	UKM, Bangi
Appears in Collections:	Faculty of Science and Technology / Fakulti Sains dan Teknologi

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