scholarly journals New weighted generalizations for differentiable exponentially convex mapping with application

2020 ◽  
Vol 5 (4) ◽  
pp. 3525-3546 ◽  
Author(s):  
Saima Rashid ◽  
◽  
Rehana Ashraf ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
...  
Keyword(s):  
Convex Mapping

scholarly journals Asymptotic Farkas lemmas for convex systems

2016 ◽  
Vol 19 (4) ◽  
pp. 160-168
Author(s):  
Dinh Nguyen ◽  
Mo Hong Tran
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Constraint Qualification ◽  
Convex Set ◽  
Lower Semicontinuous ◽  
Closed Convex Cone ◽  
Convex Mapping ◽  
Hausdorff Topological Vector Space ◽  
Reverse Convex ◽  
Locally Convex

In this paper we establish characterizations of the containment of the set {xX: xC,g(x)K}{xX: f (x)0}, where C is a closed convex subset of a locally convex Hausdorff topological vector space, X, K is a closed convex cone in another locally convex Hausdorff topological vector space and g:X Y is a K- convex mapping, in a reverse convex set, define by the proper, lower semicontinuous, convex function. Here, no constraint qualification condition or qualification condition are assumed. The characterizations are often called asymptotic Farkas-type results. The second part of the paper was devoted to variant Asymptotic Farkas-type results where the mapping is a convex mapping with respect to an extended sublinear function. It is also shown that under some closedness conditions, these asymptotic Farkas lemmas go back to non-asymptotic Farkas lemmas or stable Farkas lemmas established recently in the literature. The results can be used to study the optimization

scholarly journals On Some New Weighted Inequalities for Differentiable Exponentially Convex and Exponentially Quasi-Convex Functions with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 727 ◽  
Author(s):  
Dongming Nie ◽  
Saima Rashid ◽  
Ahmet Ocak Akdemir ◽  
Dumitru Baleanu ◽  
Jia-Bao Liu
Keyword(s):  
Numerical Analysis ◽  
Integral Inequality ◽  
Convex Functions ◽  
Random Variables ◽  
Higher Moments ◽  
Weighted Inequalities ◽  
Convex Mapping ◽  
Error Estimations ◽  
Moments Of Random Variables

In this article, we aim to establish several inequalities for differentiable exponentially convex and exponentially quasi-convex mapping, which are connected with the famous Hermite–Hadamard (HH) integral inequality. Moreover, we have provided applications of our findings to error estimations in numerical analysis and higher moments of random variables.

Horizontal path following for underactuated AUV based on dynamic circle guidance

Robotica ◽  
2015 ◽  
Vol 35 (4) ◽  
pp. 876-891 ◽  
Author(s):  
Huang Xinjing ◽  
Li Yibo ◽  
Du Fei ◽  
Jin Shijiu
Keyword(s):  
Control Method ◽  
Autonomous Underwater Vehicles ◽  
Path Following ◽  
Mapping Function ◽  
Convex Mapping ◽  
Guidance And Control ◽  
Path Following Control ◽  
And Control ◽  
Cross Track ◽  
Path Point

SUMMARYA 2D path following control method for Autonomous Underwater Vehicles (AUVs) based on dynamic circle heading modification (DCHM) is presented. The method makes a dynamic auxiliary circle, whose radius depends on the cross-track error e, to intersect the desired path to get a new expected path point, and then determines a modified expected heading for the AUV. The guidance function is achieved by a direct mapping between e and the heading modification value Ψm. Several cases are tested in order to demonstrate the performance of the guidance and control method based on DCHMs for a real AUV. Results show that methods using a convex mapping function between e and Ψm based on our new idea can easily achieve a better convergence of path following, and reduce the error between the actual and desired heading angles. We can also customize a discretionary mapping between e and Ψm to get better path following performance.

scholarly journals A family of norms with applications in quantum information theory

2011 ◽  
Vol 11 (1&2) ◽  
pp. 104-123
Author(s):  
Nathaniel Johnston ◽  
David W. Kribs
Keyword(s):  
Semidefinite Program ◽  
Constructive Proof ◽  
Convex Mapping ◽  
Semidefinite Programs ◽  
Positive Partial Transpose ◽  
The Family ◽  
Partial Transpose ◽  
Arbitrary Convex ◽  
Matlab Implementation ◽  
Werner States

We consider the problem of computing the family of operator norms recently introduced. We develop a family of semidefinite programs that can be used to exactly compute them in small dimensions and bound them in general. Some theoretical consequences follow from the duality theory of semidefinite programming, including a new constructive proof that for all r there are non-positive partial transpose Werner states that are r-undistillable. Several examples are considered via a MATLAB implementation of the semidefinite program, including the case of Werner states and randomly generated states via the Bures measure, and approximate distributions of the norms are provided. We extend these norms to arbitrary convex mapping cones and explore their implications with positive partial transpose states.

A Convex Mapping for the First Order Approach: A Note

2021 ◽  
Author(s):  
Alessandra Chirco ◽  
Corrado Benassi
Keyword(s):  
Convex Mapping ◽  
First Order

scholarly journals Some Ostrowski type inequalities via $ n $-polynomial exponentially $ s $-convex functions and their applications

2021 ◽  
Vol 6 (12) ◽  
pp. 13272-13290
Author(s):  
Muhammad Tariq ◽  
◽  
Soubhagya Kumar Sahoo ◽  
Jamshed Nasir ◽  
Hassen Aydi ◽  
...  
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Real Numbers ◽  
Convex Mapping ◽  
Positive Real ◽  
Special Means ◽  
Special Cases ◽  
Algebraic Properties

<abstract><p>This paper deals with introducing and investigating a new convex mapping namely, $ n $-polynomial exponentially $ s $-convex. Here, we present some algebraic properties and some logical examples to validate the theory of newly introduced convexity. Some novel adaptations of the well-known Hermite-Hadamard and Ostrowski type inequalities for this convex function have been established. Additionally, some special cases of the newly established results are derived as well. Finally, as applications some new limits for special means of positive real numbers are given. These new outcomes yield a few generalizations of the earlier outcomes already published in the literature.</p></abstract>

Extension Operators for Biholomorphic Mappings

2019 ◽  
Vol 62 (3) ◽  
pp. 671-679
Author(s):  
Jianfei Wang ◽  
Danli Zhang
Keyword(s):  
Unit Disk ◽  
Unbounded Domain ◽  
Geometric Approach ◽  
Starlike Function ◽  
New Method ◽  
Convex Mapping ◽  
Starlike Mapping ◽  
The Hyperbolic Metric ◽  
Image Position ◽  
Simply Connected

AbstractSuppose that $D\subset \mathbb{C}$ is a simply connected subdomain containing the origin and $f(z_{1})$ is a normalized convex (resp., starlike) function on $D$. Let $$\begin{eqnarray}\unicode[STIX]{x1D6FA}_{N}(D)=\bigg\{(z_{1},w_{1},\ldots ,w_{k})\in \mathbb{C}\times \mathbb{C}^{n_{1}}\times \cdots \times \mathbb{C}^{n_{k}}:\Vert w_{1}\Vert _{p_{1}}^{p_{1}}+\cdots +\Vert w_{k}\Vert _{p_{k}}^{p_{k}}<\frac{1}{\unicode[STIX]{x1D706}_{D}(z_{1})}\bigg\},\end{eqnarray}$$ where $p_{j}\geqslant 1$, $N=1+n_{1}+\cdots +n_{k}$, $w_{1}\in \mathbb{C}^{n_{1}},\ldots ,w_{k}\in \mathbb{C}^{n_{k}}$ and $\unicode[STIX]{x1D706}_{D}$ is the density of the hyperbolic metric on $D$. In this paper, we prove that $$\begin{eqnarray}\unicode[STIX]{x1D6F7}_{N,1/p_{1},\ldots ,1/p_{k}}(f)(z_{1},w_{1},\ldots ,w_{k})=(f(z_{1}),(f^{\prime }(z_{1}))^{1/p_{1}}w_{1},\ldots ,(f^{\prime }(z_{1}))^{1/p_{k}}w_{k})\end{eqnarray}$$ is a normalized convex (resp., starlike) mapping on $\unicode[STIX]{x1D6FA}_{N}(D)$. If $D$ is the unit disk, then our result reduces to Gong and Liu via a new method. Moreover, we give a new operator for convex mapping construction on an unbounded domain in $\mathbb{C}^{2}$. Using a geometric approach, we prove that $\unicode[STIX]{x1D6F7}_{N,1/p_{1},\ldots ,1/p_{k}}(f)$ is a spiral-like mapping of type $\unicode[STIX]{x1D6FC}$ when $f$ is a spiral-like function of type $\unicode[STIX]{x1D6FC}$ on the unit disk.

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