## Abstract and Applied Analysis

### An Extended Generalized $q$-Extensions for the Apostol Type Polynomials

#### Abstract

Through a modification on the parameters associated with generating function of the $q$-extensions for the Apostol type polynomials of order $\alpha$ and level $m$, we obtain some new results related to a unified presentation of the $q$-analog of the generalized Apostol type polynomials of order $\alpha$ and level $m$. In addition, we introduce some algebraic and differential properties for the $q$-analog of the generalized Apostol type polynomials of order $\alpha$ and level $m$ and the relation of these with the $q$-Stirling numbers of the second kind, the generalized $q$-Bernoulli polynomials of level $m$, the generalized $q$-Apostol type Bernoulli polynomials, the generalized $q$-Apostol type Euler polynomials, the generalized $q$-Apostol type Genocchi polynomials of order $\alpha$ and level $m$, and the $q$-Bernstein polynomials.

#### Article information

Source
Abstr. Appl. Anal., Volume 2018 (2018), Article ID 2937950, 13 pages.

Dates
Received: 5 February 2018
Revised: 3 May 2018
Accepted: 22 May 2018
First available in Project Euclid: 19 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1537322513

Digital Object Identifier
doi:10.1155/2018/2937950

Mathematical Reviews number (MathSciNet)
MR3827818

Zentralblatt MATH identifier
06929582

#### Citation

Castilla, Letelier; Ramírez, William; Urieles, Alejandro. An Extended Generalized $q$ -Extensions for the Apostol Type Polynomials. Abstr. Appl. Anal. 2018 (2018), Article ID 2937950, 13 pages. doi:10.1155/2018/2937950. https://projecteuclid.org/euclid.aaa/1537322513

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