In this paper sharp bounds of the third Hankel determinant for starlike and convex functions related to the exponential function are obtained, thus solving two long-standing open problems.
In this paper sharp bounds of the third Hankel determinant for starlike and convex functions related to the exponential function are obtained, thus solving two long-standing open problems.
In this study, we use the properties of convex functions, Jensen’s inequality, Holder’s inequality, and the chain rule to establish a new class of dynamic Hardy-type inequalities on time scales using delta calculus....
详细信息
This article finds q- and h-integral inequalities in implicit form for generalized convex functions. We apply the definition of q - h-integrals to establish some new unified inequalities for a class of (alpha, & h...
详细信息
This article finds q- and h-integral inequalities in implicit form for generalized convex functions. We apply the definition of q - h-integrals to establish some new unified inequalities for a class of (alpha, & hbar;- m)-convex functions. Refinements of these inequalities are given by applying a class of strongly (alpha, & hbar;- m)-convex functions. Several q-integral inequalities for various kinds of convex and strongly convex functions are deduced under specific conditions.
In this note, we give several singular value inequalities involving convex and concave functions, which can be considered as generalizations of Al-Natoor et al.'s results (J. Math. Inequal. 17:581-589, 2023). More...
详细信息
In this note, we give several singular value inequalities involving convex and concave functions, which can be considered as generalizations of Al-Natoor et al.'s results (J. Math. Inequal. 17:581-589, 2023). Moreover, some of our results are the generalizations of Al-Natoor et al.'s inequalities (Adv. Oper. Theory 9:21, 2024).
convex functions in Euclidean space can be characterized as universal viscosity subsolutions of all homogeneous fully nonlinear second order elliptic partial differential equations. This is the starting point we have ...
详细信息
convex functions in Euclidean space can be characterized as universal viscosity subsolutions of all homogeneous fully nonlinear second order elliptic partial differential equations. This is the starting point we have chosen for a theory of convex functions on the Heisenberg group.
This paper explores the relation between convex functions and the geometry of space-times and semi-Riemannian manifolds. Specifically, we study geodesic connectedness. We give geometric topological proofs of geodesic ...
详细信息
This paper explores the relation between convex functions and the geometry of space-times and semi-Riemannian manifolds. Specifically, we study geodesic connectedness. We give geometric topological proofs of geodesic connectedness for classes of space-times to which known methods do not apply. For instance: A null-disprisoning space-time is geodesically connected if it supports a proper, nonnegative strictly convex function whose critical set is a point. Timelike strictly convex hypersurfaces of Minkowski space are geodesically connected. We also give a criterion for the existence of a convex function on a semi-Riemannian manifold. We compare our work with previously known results. (C) 2017 Elsevier B.V. All rights reserved.
We introduce a new class of normalized functions univalent and convex in the unit disk. These are called convex of bounded type and the set is denoted by . For this set we find the Koebe domain, a coefficient bound, a...
详细信息
We introduce a new class of normalized functions univalent and convex in the unit disk. These are called convex of bounded type and the set is denoted by . For this set we find the Koebe domain, a coefficient bound, and a bound for . We also mention a few of the many questions that can be asked about this new class of univalent functions.
Abstract: Let $f$ be a continuous function defined on the interval $(0,1)$. For $n = 1,2, \ldots$ and $0 < s < t < 1$, denote by ${a_n}(f;s,t),{b_n}(f;s,t)$ the $n$th Fourier coefficients ...
详细信息
Abstract: Let $f$ be a continuous function defined on the interval $(0,1)$. For $n = 1,2, \ldots$ and $0 < s < t < 1$, denote by ${a_n}(f;s,t),{b_n}(f;s,t)$ the $n$th Fourier coefficients of $f|(s,t)$. It is shown that the following statements are equivalent: (i) $f$ is strictly convex on $(0,1)$. (ii) ${b_n}(f;s,t) < (2/n\pi )[f(s) - f((s + t))/2]$ for all $n = 1,2, \ldots$ and whenever $0 < s < t < 1$. (iii) ${b_n}(f;s,t) > (2/n\pi )[f((s + t)/2) - f(t)]$ for all $n = 1,2, \ldots$ and whenever $0 < s < t < 1$. If, in addition, $f$ is twice differentiable, then (i) and the following statement are also equivalent: (iv) ${a_n}(f;s,t) > 0$ for all $n = 1,2, \ldots$ and whenever $0 < s < t < 1$.
For the well developed notion of approximate Birkhoff-James orthogonality, in a real or complex normed linear space, we formulate a new characterization. It can be derived from other, already known, characterizations ...
详细信息
For the well developed notion of approximate Birkhoff-James orthogonality, in a real or complex normed linear space, we formulate a new characterization. It can be derived from other, already known, characterizations as well as obtained in a more elementary and direct way, on the basis of some simple inequalities for real convex functions.
We investigate the topological structure of Alexandrov surfaces of curvature bounded below which possess convex functions. We do not assume the continuities of these functions. Nevertheless, if the convex functions sa...
详细信息
We investigate the topological structure of Alexandrov surfaces of curvature bounded below which possess convex functions. We do not assume the continuities of these functions. Nevertheless, if the convex functions satisfy a condition of local nonconstancy, then the topological structures of Alexandrov surfaces and the level sets configurations of these functions in question are determined.
暂无评论