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In this paper, we study classes of discrete convex functions: submodular functions on modular semilattices and L-convex functions on oriented modular graphs. They were introduced by the author in complexity classification of minimum…
We extend deconvolution in a periodic setting to deal with functional data. The resulting functional deconvolution model can be viewed as a generalization of a multitude of inverse problems in mathematical physics where one needs to recover…
In this paper, we obtain the subadditivity inequality of strongly operator convex functions on $(0, \infty)$ and $(-\infty,0)$. Applying the properties of operator convex functions, we deduce the subadditivity property of operator monotone…
We consider the problem of maximizing a convex function over a closed convex set in a real Hilbert space. For linear functions, we show that a single orthogonal projection suffices to obtain an approximate solution. For continuous convex…
Subdifferentials (in the sense of convex analysis) of matrix-valued functions defined on $\mathbb{R}^d$ that are convex with respect to the L\"{o}wner partial order can have a complicated structure and might be very difficult to compute…
In this paper, we prove some new inequalities of Simpson's type for functions whose derivatives of absolute values are h-convex and h-concave functions. Some new estimations are obtained. Also we give some sophisticated results for some…
In this paper, a general integral identity for convex functions is derived. Then, we establish new some inequalities of the Simpson and the Hermite-Hadamard's type for functions whose absolute values of derivatives are convex. Some…
This paper studies the convexity properties of nonsmooth extended-real-valued weakly convex functions, a class of functions that is central to modern optimization and its applications. We establish new characterizations of convexity using…
In this paper, the authors establish some new estimates for the remainder term of the midpoint, trapezoid, and Simpson formula using functions whose derivatives in absolute value at certain power are s-convex. Some applications to special…
In this note, we establish the Lipschitz continuity of finite-dimensional globally convex functions on all given balls and global Lipschitz continuity for eligible functions of that type. The Lipschitz constants in both situations draw…
Discrete Fenchel duality is one of the central issues in discrete convex analysis. The Fenchel-type min-max theorem for a pair of integer-valued M-natural-convex functions generalizes the min-max formulas for polymatroid intersection and…
In this article we pose the problem of existence and uniqueness of convex body for which the projection curvature radius function coincides with given function. We find a necessary and sufficient condition that ensures a positive answer to…
In this paper, we establish new general inequality for convex functions. Then we apply this inequality to obtain the midpoint, trapezoid and averaged midpoint-trapezoid integral inequality. Also, some applications for special means of real…
The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…
We study the smooth structure of convex functions by generalizing a powerful concept so-called self-concordance introduced by Nesterov and Nemirovskii in the early 1990s to a broader class of convex functions, which we call generalized…
This paper explores a natural generalization of Euclidean projection through the lens of strongly quasiconvex functions, as developed in prior works. By establishing a connection between strongly quasiconvex functions and the theory of…
In this paper, we study the properties of integral functionals induced on $L^1_E (S,\mu)$ by closed convex functions on a Euclidean space $E$. We give sufficient conditions for such integral functions to be strongly rotund (well-posed). We…
This paper studies the projected saddle-point dynamics associated to a convex-concave function, which we term saddle function. The dynamics consists of gradient descent of the saddle function in variables corresponding to convexity and…
We give a characterization of smooth, rotation and dually epi-translation invariant valuations and use this result to obtain a new proof of the Hadwiger theorem on convex functions. We also give a description of the construction of the…
In this article we consider a consistent convex feasibility problem in a real Hilbert space defined by a finite family of sets $C_i$. We are interested, in particular, in the case where for each $i$, $C_i=Fix (U_i)=\{z\in \mathcal H\mid…