Identities on Some Special Poynomials Derived from the Concepts of n-Normed Structures, Accretive Operators and Contraction Mappings - Kır, Mehmet; Dutta, Hemen; Açikgöz, Mehmet; Aracı, Serkan (IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, 2018)
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 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.
Keywords: n-Normed space; Fixed point; Non-expansive mapping; Contraction mapping; Accretive operator; Resolvent operator; Yosida's approximation; q-Genocchi polynomials with weight zero; Frobenius-Euler polynomials