In the paper, we derive some new symmetric identities of q-Genocchi polynomials arising from the fermionic p-adic q-integral on Z(p).

In this paper, we study the notions of accretive operators, contraction mappings, non-expansive mappings using the idea of n (>l)-normed structures for some relevant results. Further, we define (lambda, q)-transform by ...

We introduce the Hermite based poly-Bernoulli polynomials with a q parameter and give some of their basic properties including not only addition property, but also derivative properties and integral representations. We ...

The Newton power-sum formulas relate to sums of powers of roots of a polynomial with the coefficients of the polynomial. In this paper we obtain formulas that relate to sums of reciprocal powers of zeros and poles of entire ...

The main purpose of this article is to introduce a general class of the three-variable unified Apostol-type q-polynomials and to investigate their properties and characteristics. In particular, the generating function, ...

The significance of multi-variable special polynomials has been identified both in mathematical and applied frameworks. The article aims to focus on a new class of 3-variable Legendre-truncated-exponential-based Sheffer ...

We establish fractional integral and derivative formulas by using fractional calculus operators involving the extended generalized Mathieu series. Next, we develop their composition formulas by applying the integral ...

In the present paper, we find the Fourier expansion of the Apostol Frobenius-Euler polynomials. By using a Fourier expansion of the Apostol Frobenius-Euler polynomials, we derive some new and interesting results.

In this work, we study the asymptotic properties of a new Sturm-Liouville problem with retarded argument. Contrary to previous works, differential equation includes eigenparameter as a quadratic function. In the considered ...

In this paper, we develop the theory of the multiple q-analogue of the Heine's binomial formula, chain rule and Leibniz's rule. We also derive many useful definitions and results involving multiple q-antiderivative and ...