Identities on Some Special Poynomials Derived from the Concepts of $$ {\it n}$$ n -Normed Structures, Accretive Operators and Contraction Mappings

Abstract

In this paper, we study the notions of accretive operators, contraction mappings, non-expansive mappings using the idea of n (>1)-normed structures for some relevant results. Further, we define \(\left( \lambda ,q\right) \)-transform by utilizing the definition of the generating function of q-Genocchi polynomials with weight zero to construct interesting properties related to q-Genocchi polynomials with weight zero and Frobenius–Euler polynomials. Furthermore, we describe p-adic q-\( \lambda \)-transform of higher order and construct a link between q-Genocchi polynomials of higher order with weight zero and higher order Frobenius–Euler polynomials using this transform. Our applications in this paper provide a link between analytic numbers theory and n-normed spaces.