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According to the great mathematician Henri Lebesgue, making direct comparisons of objects with regard to a property is a fundamental mathematical process for deriving measurements. Measuring objects by using a known scale first then comparing the measurements works well for properties for which scales of measurement exist. The theme of this paper is that direct comparisons are necessary to establish...
Let K be a quadratic field, and let ζK its Dedekind zeta function. In this paper we introduce a factorization of ζK into two functions, L1 and L2, defined as partial Euler products of ζK, which lead to a factorization of Riemann’s ζ function into two functions, p1 and p2. We prove that these functions satisfy a functional equation which has a unique solution, and we give series of very...
In this paper, we define random Lie $$C^*$$ C ∗ -algebras, then we apply a fixed point theorem to investigate some new stability results for $$(\alpha ,\beta ,\gamma )$$ ( α , β , γ ) -derivations on random Lie $$C^*$$ C ∗ -algebras associated with a generalized Cauchy–Jensen type additive functional equation.
The main propose of this article is to investigate and modify Hermite type polynomials, Milne-Thomson type polynomials and Poisson–Charlier type polynomials by using generating functions and their functional equations. By using functional equations of the generating functions for these polynomials, we not only derive some identities and relations including the Bernoulli numbers and polynomials, the...
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