A NONLINEAR COMPLEMENTARITY-TYPE PROBLEM AND VARIATIONAL-TYPE INEQUALITY

2016 ◽  
Vol 11 (1) ◽  
pp. 1-21
Author(s):  
Mitali Routaray ◽  
A. Behera
Keyword(s):  
Type Inequality ◽  
Type Problem ◽  
Nonlinear Complementarity ◽  
Variational Type

scholarly journals A quantitative reverse Faber-Krahn inequality for the first Robin eigenvalue with negative boundary parameter

2020 ◽  
Author(s):  
Simone Cito ◽  
Domenico Angelo La Manna
Keyword(s):  
Convex Sets ◽  
Type Inequality ◽  
First Eigenvalue ◽  
Type Problem ◽  
Laplacian Eigenvalue ◽  
Quantitative Form ◽  
Boundary Parameter ◽  
Robin Laplacian ◽  
Krahn Inequality ◽  
Optimal Set

The aim of this paper is to prove a quantitative form of a reverse Faber-Krahn type inequality for the first Robin Laplacian eigenvalue λ β with negative boundary parameter among convex sets of prescribed perimeter. In that framework, the ball is the only maximizer for λ β and the distance from the optimal set is considered in terms of Hausdorff distance. The key point of our stategy is to prove a quantitative reverse Faber-Krahn inequality for the first eigenvalue of a Steklov-type problem related to the original Robin problem.

A Variational-Type Inequality

OPSEARCH ◽  
1999 ◽  
Vol 36 (2) ◽  
pp. 107-112
Author(s):  
A. Behera ◽  
Lopamudra Nayak
Keyword(s):  
Type Inequality ◽  
Variational Type

scholarly journals A spherical rearrangement proof of the stability of a Riesz-type inequality and an application to an isoperimetric type problem

2021 ◽  
Author(s):  
Giacomo Ascione
Keyword(s):  
Isoperimetric Inequality ◽  
Type Inequality ◽  
Stability Result ◽  
Global Minimizer ◽  
Mass Transportation ◽  
Volume Constraint ◽  
Type Problem ◽  
Fixed Volume ◽  
The Stability ◽  
Perimeter Penalization

We prove the stability of the ball as global minimizer of an attractive shape functional under volume constraint, by means of mass transportation arguments. The stability exponent is $1/2$ and it is sharp. Moreover, we use such stability result together with the quantitative (possibly fractional) isoperimetric inequality to prove that the ball is a global minimizer of a shape functional involving both an attractive and a repulsive term with a sufficiently large fixed volume and with a suitable (possibly fractional) perimeter penalization.

scholarly journals Bounds on the solution of a Cauchy-type problem involving a weighted sequential fractional derivative

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Khaled Furati
Keyword(s):  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Type Inequality ◽  
Gauss Hypergeometric Function ◽  
Cauchy Type ◽  
Type Problem ◽  
Sequential Fractional Derivative ◽  
Cauchy Type Problem ◽  
Fractional Differential ◽  
Bounds On The Solution

AbstractIn this paper we establish some bounds for the solution of a Cauchytype problem for a class of fractional differential equations with a weighted sequential fractional derivative. The bounds are based on a Bihari-type inequality and a bound on the Gauss hypergeometric function.

scholarly journals Local Sharp Vector Variational Type Inequality and Optimization Problems

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1844
Author(s):  
Jong Kyu Kim ◽  
Salahuddin
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Type Inequality ◽  
Efficient Solutions ◽  
Vector Optimization Problems ◽  
Lipschitzian Functions ◽  
Locally Lipschitzian Functions ◽  
The Relationship ◽  
Variational Type ◽  
Convexity Conditions

In this paper, our goal was to establish the relationship between solutions of local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, also Minty local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, under generalized approximate η-convexity conditions for locally Lipschitzian functions.

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