Browsing by Author "Khan, Muhammad Ghaffar"
Now showing items 1-5 of 5
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Applications of q-Derivative Operator to the Subclass of Bi-Univalent Functions Involving q-Chebyshev Polynomials
Khan, Bilal; Liu, Zhi-Guo; Shaba, Timilehin Gideon; Araci, Serkan; Khan, Nazar; Khan, Muhammad Ghaffar (HINDAWI LTD, MAR 18 202)In recent years, the usage of the q-derivative and symmetric q-derivative operators is significant. In this study, firstly, many known concepts of the q-derivative operator are highlighted and given. We then use the symmetric ... -
Applications of q-hermite polynomials to subclasses of analytic and bi-univalent functions
Zhang, Caihuan; Khan, Bilal; Shaba, Timilehin Gideon; Ro, Jong-Suk; Araci, Serkan; Khan, Muhammad Ghaffar (MDPI, August 202)In mathematics, physics, and engineering, orthogonal polynomials and special functions play a vital role in the development of numerical and analytical approaches. This field of study has received a lot of attention in ... -
Coefficient Estimates for a Subclass of Meromorphic Multivalent q-Close-to-Convex Functions
Shi, Lei; Ahmad, Bakhtiar; Khan, Nazar; Khan, Muhammad Ghaffar; Araci, Serkan; Mashwani, Wali Khan; Khan, Bilal (MDPI, OCT 2021)By making use of the concept of basic (or q-) calculus, many subclasses of analytic and symmetric q-starlike functions have been defined and studied from different viewpoints and perspectives. In this article, we introduce ... -
A subclass of meromorphic Janowski-type multivalent q-starlike functions involving a q-differential operator
Ahmad, Bakhtiar; Mashwani, Wali Khan; Aracı, Serkan; Mustafa, Saima; Khan, Muhammad Ghaffar; Khan, Bilal (Springer Nature, 2022)Keeping in view the latest trends toward quantum calculus, due to its various applications in physics and applied mathematics, we introduce a new subclass of meromorphic multivalent functions in Janowski domain with the ... -
Third Hankel Determinant for the Logarithmic Coefficients of Starlike Functions Associated with Sine Function
Khan, Bilal; Aldawish, Ibtisam; Araci, Serkan; Khan, Muhammad Ghaffar (MDPI, MAY 2022)The logarithmic functions have been used in a verity of areas of mathematics and other sciences. As far as we know, no one has used the coefficients of logarithmic functions to determine the bounds for the third Hankel ...
