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23. A subclass of meromorphic Janowski-type multivalent q-starlike functions involving a q-differential operator.

Author

Ahmad, Bakhtiar, Mashwani, Wali Khan, Araci, Serkan, Mustafa, Saima, Khan, Muhammad Ghaffar, and Khan, Bilal

Subjects
ALGEBRAIC functions, APPLIED mathematics, MEROMORPHIC functions, MATHEMATICAL physics, STAR-like functions, CALCULUS
Abstract

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 help of the q-differential operator. Furthermore, we investigate some useful geometric and algebraic properties of these functions. We discuss sufficiency criteria, distortion bounds, coefficient estimates, radius of starlikeness, radius of convexity, inclusion property, and convex combinations via some examples and, for some particular cases of the parameters defined, show the credibility of these results. [ABSTRACT FROM AUTHOR]

Published
2022
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24. A New Approach to -Bernoulli Numbers and -Bernoulli Polynomials Related to -Bernstein Polynomials

Author

Açikgöz Mehmet, Erdal Dilek, and Araci Serkan

Subjects
Mathematics, QA1-939
Abstract

We present a new generating function related to the -Bernoulli numbers and -Bernoulli polynomials. We give a new construction of these numbers and polynomials related to the second-kind Stirling numbers and -Bernstein polynomials. We also consider the generalized -Bernoulli polynomials attached to Dirichlet's character and have their generating function . We obtain distribution relations for the -Bernoulli polynomials and have some identities involving -Bernoulli numbers and polynomials related to the second kind Stirling numbers and -Bernstein polynomials. Finally, we derive the -extensions of zeta functions from the Mellin transformation of this generating function which interpolates the -Bernoulli polynomials at negative integers and is associated with -Bernstein polynomials.

Published
2010

25. A New Approach to <graphic file='1687-1847-2010-951764-i1.gif'/>-Bernoulli Numbers and <graphic file='1687-1847-2010-951764-i2.gif'/>-Bernoulli Polynomials Related to <graphic file='1687-1847-2010-951764-i3.gif'/>-Bernstein Polynomials

Author

Açikgöz Mehmet, Erdal Dilek, and Araci Serkan

Subjects
TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES, lcsh:Mathematics, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Data_FILES, lcsh:QA1-939
Abstract

We present a new generating function related to the -Bernoulli numbers and -Bernoulli polynomials. We give a new construction of these numbers and polynomials related to the second-kind Stirling numbers and -Bernstein polynomials. We also consider the generalized -Bernoulli polynomials attached to Dirichlet's character and have their generating function . We obtain distribution relations for the -Bernoulli polynomials and have some identities involving -Bernoulli numbers and polynomials related to the second kind Stirling numbers and -Bernstein polynomials. Finally, we derive the -extensions of zeta functions from the Mellin transformation of this generating function which interpolates the -Bernoulli polynomials at negative integers and is associated with -Bernstein polynomials.

Published
2010

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