Related papers: Sequential derivatives
A new notion of metric differentiability of set-valued functions at a point is introduced in terms of right and left limits of special set-valued metric divided differences of first order. A local metric linear approximant of a metrically…
In 2011, Gun, Murty and Rath studied non-vanishing and transcendental nature of special values of a varying class of $L$-functions and their derivatives. This led to a number of works by several authors in different set-ups including…
A new derivative, called deformable derivative, is introduced here which is equivalent to ordinary derivative in the sense that one implies other. The deformable derivative is defined using limit approach like that of ordinary one but with…
We show that a substantial portion of stochastic calculus can be developed along similar lines to ordinary calculus, with derivative-based concepts driving the development. We define a notion of stopping derivative, which is a form of right…
Two approximations, derived from continuous expansions of Riemann-Liouville fractional derivatives into series involving integer order derivatives, are studied. Using those series, one can formally transform any problem that contains…
The concept of sequential choice functions is introduced and studied. This concept applies to the reduction of the problem of stable matchings with sequential workers to a situation where the workers are linear.
The main aim of this note is to provide characterization theorems concerning real derivations. Among others the following implication will be verified: Assume that $\xi\colon \mathbb{R}\to \mathbb{R}$ is a given differentiable function and…
The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment…
The function spaces of continuously differentiable functions are extensively studied and appear in various mathematical settings. In this context, we investigate the spaces of continuously fractional differentiable functions of order…
We define a proper differential sequence of ordinary differential equations and introduce a method to derive an alternative sequence of integrals for such a sequence. We describe some general properties which are illustrated by several…
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
Sequential modelling entails making sense of sequential data, which naturally occurs in a wide array of domains. One example is systems that interact with users, log user actions and behaviour, and make recommendations of items of potential…
We discuss the functional lazy techniques in generation and handling of arbitrarily long sequences of derivatives of numerical expressions in one ``variable''; the domain to which the paper belongs is usually nicknamed ``Automatic…
This paper treats the variation of sets. We attempt to formulate convergence and continuity of set-valued functions in a different way from the theories on sequences of sets and correspondence. In the final section, we also attempt to…
We introduce a notion of fractional (noninteger order) derivative on an arbitrary nonempty closed subset of the real numbers (on a time scale). Main properties of the new operator are proved and several illustrative examples given.
Splitting of sequential data, such as videos and time series, is an essential step in various data analysis tasks, including object tracking and anomaly detection. However, splitting sequential data presents a variety of challenges that can…
We introduce the notion of Differential Sequences of ordinary differential equations. This is motivated by related studies based on evolution partial differential equations. We discuss the Riccati Sequence in terms of symmetry analysis,…
It is obtained necessary and sufficient conditions of dependence on $\aleph$ coordinates for functions of several variables, each of which is a product of metrizable factors. The set of discontinuity points of such functions is…
We study various proofs of the caracterization of constant functions, more precisely of the theorem: a derivable function, defined on a real interval, is constant if, and only if, its derivative is null. Our aim is to study the…
In this paper, we introduce a new generalized derivative, which we term the specular derivative. We establish the Quasi-Rolles' Theorem, the Quasi-Mean Value Theorem, and the Fundamental Theorem of Calculus in light of the specular…