This paper introduces a complete Gn-Menger space and defines the Hausdorff–Pompeiu distance in space. Furthermore, we show novel fixed-point theorem for Gn-Menger-θ-contractions fractal spaces.

We suggest an explicit continuation formula for a solution to the Cauchy problem Poisson equation in domain from its values and of normal derivative on part boundary. construct this based Carleman--Yarmuhamedov function method.

This paper classifies the sequences that satisfy a generalization of the Cauchy determinant formula. They are the generalized Fibonacci numbers, up to a scalar multiple. Following this, it is determined which of these sequences generate Hankel matrices of unit fractions with integer inverses. As a corollary we obtain another proof that the Filbert Matrix has an inverse with integer entries, com...

An extension of Kato’s stability condition for nonautonomous Cauchy problems is presented. It is proved that in the commutative case this condition and a mild regularity assumption imply wellposedness. If one supposes the Kato-stability, then the solutions are given by an integral formula. By means of examples we show that in general these stability conditions cannot be omitted in our results. ...

We study the backward shift operator on Hilbert spaces Hα (for α ≥ 0) which are norm equivalent to the Dirichlet-type spaces Dα. Although these operators are unitarily equivalent to the adjoints of the forward shift operator on certain weighted Bergman spaces, our approach is direct and completely independent of the standard Cauchy duality. We employ only the classical Hardy space theory and an...

In this paper we offer a new definition of monogenicity for functions defined on R with values in the Clifford algebra Rn following an idea inspired by the recent papers [6], [7]. This new class of monogenic functions contains the polynomials (and, more in general, power series) with coefficients in the Clifford algebra Rn. We will prove a Cauchy integral formula as well as some of its conseque...

Chen’s lemma on iterated integrals implies that certain identities involving multiple integrals, such as the de Bruijn and Wick formulas, amount to combinatorial identities for Pfaffians and hafnians in shuffle algebras. We provide direct algebraic proofs of such shuffle identities, and obtain various generalizations. We also discuss some Pfaffian identities due to Sundquist and Ishikawa-Wakaya...

In this paper, we give new generating functions which produce Barnes' type multiple generalized Changhee q-Bernoulli polynomials and poly-nomials. These functions are very important to construct multiple zeta functions. By using Mellin transform's formula and Cauchy Theorem , we prove the analytic continuation of Barnes' type multiple Changhee q-zeta function. Finally we give some relations bet...

This paper investigates the pricing formula for barrier options where underlying asset is driven by sub-mixed fractional Brownian motion with jump. By applying corresponding Ito^’s formula, B-S type PDE derived a self-financing strategy. Furthermore, explicit obtained through converting to Cauchy problem. Numerical experiments are conducted test impact of price, Hurst index, jump intensity and ...

323 Caudill Jr, L.F. and B.D. Lowe, On the construction of a potential from Cauchy data, Journal of Computational and Applied Mathematics 47 (1993) 323-333. We investigate the problem of recovering a potential q(y) in the differential equation: Llu + q(y)u = 0, (x, y)E(O, l)x(O, 1), u(O, y)=u(l, y)=u(x,0)=0, u(x, l)= f(x), u/x, 1)= g(x). The method of separation of variables reduces the recover...