Related papers: From Quasidifferentiable to Directed Subdifferenti…

We define a simplicial differential calculus by generalizing divided differences from the case of curves to the case of general maps, defined on general topological vector spaces, or even on modules over a topological ring K. This calculus…

Quasianalytic classes are classes of infinitely differentiable functions that satisfy the analytic continuation property enjoyed by analytic functions. Two general examples are quasianalytic Denjoy-Carleman classes (of origin in the…

We generalize the classical Bernstein theorem concerning the constructive description of classes of functions uniformly continuous on the real line. The approximation of continuous bounded functions by entire functions of exponential type…

We identity the optimal non-infinitesimal direction of descent for a convex function. An algorithm is developed that can theoretically minimize a subset of (non-convex) functions.

Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In…

Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…

We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…

We provide a first-order necessary and sufficient condition for optimality of lower semicontinuous functions on Banach spaces using the concept of subdifferential. From the sufficient condition we derive that any subdifferential operator is…

We derive some formulas that rule the behaviour of finite differences under composition of functions with vector values and arguments.

We describe a generalization of Gabriel and Zisman's Calculus of Fractions to quasicategories, showing that the two essentially coincide for the nerve of a category. We then prove that the marked Ex-functor can be used to compute the…

In this paper we study the radial epiderivative notion for nonconvex functions, which extends the (classical) directional derivative concept. The paper presents new definition and new properties for this notion and establishes relationships…

This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and…

The fractional calculus of variations is now a subject under strong research. Different definitions for fractional derivatives and integrals are used, depending on the purpose under study. In this paper the fractional operators are defined…

Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…

In this article we determine the coefficient bounds for functions in certain subclasses of analytic functions defined by subordination which are related to the well-known classes of starlike and convex functions. The main results deal with…

We construct a class of real-valued nonnegative binary functions on a set of jointly distributed random variables, which satisfy the triangle inequality and vanish at identical arguments (pseudo-quasi-metrics). These functions are useful in…

This paper presents a self-contained new theory of weak fractional differential calculus and fractional Sobolev spaces in one-dimension. The crux of this new theory is the introduction of a weak fractional derivative notion which is a…

Holderian functions have strong non-linearities, which result in singularities in the derivatives. This manuscript presents several fractional-order Taylor expansions of H\"olderian functions around points of non- differentiability. These…

Extended real-valued functions are often used in optimization theory, but in different ways for infimum problems and for supremum problems. We present an approach to extended real-valued functions that works for all types of problems and…

In this work we present a novel proof of the Saalschutz formula by using the theory of discrete fractional calculus. The proofs of some results within this theory, namely, the fractional power rule and the fractional Leibniz rule are…