Related papers: Second-order differential subordinations for analy…
In this article, by making use of the linear operator introduced and studied by Srivastava and Attiya \cite{srivastava1}, suitable classes of admissible functions are investigated and the dual properties of the third-order differential…
We study differentiable strongly quasiconvex functions for providing new properties for algorithmic and monotonicity purposes. Furthemore, we provide insights into the decreasing behaviour of strongly quasiconvex functions, applying this…
In this note we investigate the inclusion relationship between the class of strongly starlike functions of order alpha and type beta and the class of strongly convex functions of order alpha and type beta which are subclass of normalized…
A new integral identity for functions with continuous second partial derivatives is derived. It is shown that the value of any function f(r,t) at position r and time t is completely determined by its previous values at all other locations…
It is well-known that every convex function admits an affine support at every interior point of a domain. Convex functions of higher order (precisely of an odd order) have a similar property: they are supported by the polynomials of degree…
In this paper, we obtain some companions of Ostrowski type inequality for absolutely continuous functions whose second derivatives absolute value are convex and concave.Finally, we gave some applications for special means.
Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the…
Second-order variational properties have been shown to play important theoretical and numerical roles for different classes of optimization problems. Among such properties, twice epi-differentiability has a special place because of its…
In this paper, we introduce some analytical techniques to solve some classes of second order differential equations. Such classes of differential equations arise in describing some mathematical problems in Physics and Engineering.
This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with…
In this paper it is shown that higher order quasiconvex functions suitable in the variational treatment of problems involving second derivatives may be extended to the space of all matrices as classical quasiconvex functions. Precisely, it…
In the present paper, we derive the third-order differential subordination and superordination results for some analytic univalent functions defined in the unit disc. These results are associated with generalized Struve functions and are…
We observe that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In addition, we describe numerical experiments which illustrate…
Under certain conditions, we obtain sharp bounds on some functionals defined in the coefficient space of starlike functions. It has been found that the functionals are closely associated with certain coefficient problems, which are of…
We perform conformal perturbation theory by marginal operators to first order. A suitable renormalization method is needed that makes the conformal invariance of the deformed correlation functions manifest. Combining the embedding space…
Let $\mathcal{A}$ be the family of analytic and normalized functions in the open unit disc $|z|<1$. In this article we consider the following classes \begin{equation*} \mathcal{R}(\alpha,\beta):=\left\{ f\in \mathcal{A}: {\rm…
In this paper, we study optimization methods consisting of iteratively minimizing surrogates of an objective function. By proposing several algorithmic variants and simple convergence analyses, we make two main contributions. First, we…
An irreducible canonical approach to second-order reducible second-class constraints is given. The procedure is exemplified on gauge-fixed three-forms.
We report a new analytical method for solution of a wide class of second-order differential equations with eigenvalues replaced by arbitrary functions. Such classes of problems occur frequently in Quantum Mechanics and Optics. This approach…
We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…