Related papers: Hadamard Inverse Function Theorem Proved by Variat…
We introduce a notion of a noncommutative function defined on a domain of $d$-tuples of bounded operators on an infinite dimensional Hilbert space. Inverse and implicit function theorems in this setting are established. When these…
Ackermann's function can be expressed using an iterative algorithm, which essentially takes the form of a term rewriting system. Although the termination of this algorithm is far from obvious, its equivalence to the traditional recursive…
In this paper, we establish several new convex dominated functions and then we obtain new Hadamard type inequalities.
We give a survey of the Lagrange inversion formula, including different versions and proofs, with applications to combinatorial and formal power series identities.
In this paper, a general form of integral inequalities of Hermite-Hadamard's type through differentiability for s-Convex function in second sense and whose all derivatives are absolutely continuous are established. The generalized integral…
We give here a new proof of a Tauberian Theorem of complex Laplace transform using the Theory of measure and theory of function with bounded variations. However we deduce the simple proof of Prime Number Theorem.
Freed-Hopkins-Teleman expressed the Verlinde algebra as twisted equivariant K-theory. We study how to recover the full system (fusion algebra of defect lines), nimrep (cylindrical partition function), etc of modular invariant partition…
We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also…
The "odd transgression" introduced by the authors in an earlier article is applied to construct and study the inverse image functor in the theory of Courant algebroids.
This paper aims to characterize the function appearing in the weighted Hermite-Hadamard inequality. We provide improved inequalities for the weighted means as applications of the obtained results. Modifications of the weighted…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
We consider an inverse extremal problem for variational functionals on arbitrary time scales. Using the Euler-Lagrange equation and the strengthened Legendre condition, we derive a general form for a variational functional that attains a…
We show that many infinite classes of permutations over finite fields can be constructed via translators with a large choice of parameters. We first charac- terize some functions having linear translators, based on which several families of…
In this paper, we consider a new class of convex functions which is called $\lambda$-preinvex functions. We prove several Hermite-Hadamard type inequalities for differentiable $\lambda$-preinvex functions via Fractional Integrals. Some…
The authors study the classical Lagrange inversion theorem--an antecedent of the modern implicit function theorem--in the smooth case. Examples are given to show that the result is sharp.
In the present work, firstly, we use a minimax equality to prove the existence of a solution of certain system of varitional equations and we provide a numerical approximation of such a solution. Then, we propose a numerical method to solve…
This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…
In this paper, new integral inequalities of Hadamard type involving several differentiable \Phi-r-convex functions are given.
Many different types of fractional calculus have been defined, which may be categorised into broad classes according to their properties and behaviours. Two types that have been much studied in the literature are the Hadamard-type…
The following paper follows on from work by Kamae, and gives a rigorous proof of the Ergodic Theorem, using nonstandard analysis.