HARMONIC MULTIVALENT FUNCTIONS ASSOCIATED WITH A -ANALOGUE OF RUSCHEWEYH OPERATOR

• Published in: TWMS journal of applied and engineering mathematics Vol. 13; no. 3; p. 1164
• Main Authors: Sharma, P, Mishra, O, Ahuja, O.P, Cetinkaya, A
• Format: Journal Article
• Language: English
• Published: Istanbul Turkic World Mathematical Society 01.01.2023; Elman Hasanoglu
• Subjects: Calculus; Convexity; Mathematics; Questions and answers
• ISSN: 2146-1147; 2146-1147

The aim of this paper is to introduce and investigate a new class of harmonic multivalent functions defined by (p,q)-analogue of Ruscheweyh operator for multivalent functions. For this new class, we obtain a (p,q)-coefficient inequality as a sufficient condition. Using this coefficient inequality, we establish sharp bounds of the real parts of the ratios of harmonic multivalent functions to its sequences of partial sums. We further consider a subclass of our new class and for which we obtain (p,q)-analogue of coefficient characterization which in fact helps us to determine its properties such as distortion bounds, extreme points, convolutions and convexity conditions. In the last section on conclusion, it is pointed out that the results obtained in this paper may also be extended to some generalized classes. Keywords: (p,q)-calculus; (p,q)-Ruscheweyh operator; multivalent harmonic functions; a (p,q)-Ruscheweyh multivalent operator; partial sums. AMS Subject Classification: 30C45; 30C50; 30C80.