Related papers: Improved eigenvalue inequalities via two major sub…

This paper studies the log-convexity of the extended beta functions. As a consequence, Tur\'an-type inequalities are established.The monotonicity, log-convexity, log-concavity of extended hypergeometric functions are deduced by using the…

We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization. The problem is closely related to decomposable submodular function minimization and arises in many learning on graphs and…

In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…

The aim of this work is to provide formulae for the subdifferential and the conjungate function of the supremun function over an arbitrary family of functions. The work is principally motivated by the case when data functions are lower…

This paper concerns three classes of real-valued functions on intervals, operator monotone functions, operator convex functions, and strongly operator convex functions. Strongly operator convex functions were previously treated in [3] and…

Using convexity and superquadracity we extend in this paper Euler Lagrange identity, Bohr's inequalitiy and the triangle inequality.

In this note we provide a full conjugacy and subdifferential calculus for convex convex-composite functions in finite-dimensional space. Our approach, based on infimal convolution and cone-convexity, is straightforward and yields the…

In this paper, we establish some integral ineuqalities for n- times differentiable quasi-convex functions.

In this work, several sharp bounds for the \v{C}eby\v{s}ev functional involving various type of functions are proved. In particular, for the \v{C}eby\v{s}ev functional of two absolutely continuous functions whose first derivatives are both…

We study arithmetic inequalities for multiplicative, sub(super)-multiplicative, sub(super)-homogeneous functions. Applications for the classical arithmetic functions are pointed out.

This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of)…

In this paper, we study constraint qualifications for the nonconvex inequality defined by a proper lower semicontinuous function. These constraint qualifications involve the generalized construction of normal cones and subdifferentials.…

In this paper, we give some definitions on quasi-convex functions and we prove inequalities contain J-quasi-convex and W-quasi-convex functions. We give also some inclusions.

The paper addresses the study and applications of a broad class of extended-real-valued functions, known as optimal value or marginal functions, which are frequently appeared in variational analysis, parametric optimization, and a variety…

A new directional derivative and a new subdifferential for set-valued convex functions are constructed, and a set-valued version of the so-called 'max-formula' is proven. The new concepts are used to characterize solutions of convex…

In this paper, we obtained some inequalities for \phi_{s}-convex function, \phi-Godunova-Levin function, \phi-P-function and log-\phi-convex function. Finally, we defined the class of \phi-quasi-convex functions and we examined some…

A class of functions involving the divided differences of the psi function and the polygamma functions and originating from Kershaw's double inequality are proved to be completely monotonic. As applications of these results, the…

Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and numerically tested. The methods combine advantages of the two-grid algorithm, two-space method, the shifted inverse power method, and the polynomial…

This article studies the problem whether two convex (concave) regression functions modelling the relation between a response and covariate in two samples differ by a shift in the horizontal and/or vertical axis. We consider a nonparametric…

In this paper, a class of generalized backward doubly stochastic differential equations whose coefficient contains the subdifferential operators of two convex functions (also called generalized backward doubly stochastic variational…