In this article, we consider Jain-Durrmeyer operators associated with the Apostol-Genocchi polynomials and study approximation properties of these Durrmeyer operators. Furthermore, examine behaviour including K-functional. We estimate rate convergence proposed for function in Lipschitz-type space local results by using modulus continuity. Employing Mathematica software, to show absolute error g...

We propose certain Durrmeyer-type operators for Apostol-Genocchi polynomials in this research. We explore these operators' approximation attributes and measure the rate of convergence. In addition, we present a direct theorem based on first second-order modulus continuity, local findings Lipschitz class functions typical continuity. Finally, showed graph illustratin...

A new q-analog of Genocchi numbers is introduced through a q-analog of Seidel’s triangle associated to Genocchi numbers. It is then shown that these q-Genocchi numbers have interesting combinatorial interpretations in the classical models for Genocchi numbers such as alternating pistols, alternating permutations, non intersecting lattice paths and skew Young tableaux.

Utilizing p,q-numbers and p,q-concepts, in 2016, Duran et al. considered p,q-Genocchi numbers polynomials, p,q-Bernoulli polynomials p,q-Euler provided multifarious formulas properties for these polynomials. Inspired motivated by this consideration, many authors have introduced (p,q)-special described some of their applications. In paper, using the (p,q)-cosine (p,q)-sine we consider a novel ki...