scholarly journals On the stability of solution mappings parametric generalized vector quasivariational inequality problems of the Minty type

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 747-757 ◽  
Author(s):  
Lam Anh ◽  
Hung van

In this paper, we study two parametric weak and strong vector quasivariational inequality problems of the Minty type. The stability properties of the exact solution sets and approximate solution sets for these problems such as the upper semicontinuity, the lower semicontinuity, the Hausdorff lower semicontinuity, the continuity and the Hausdorff continuity are obtained. The results presented in the paper improve and extend the main results in the literature.

In this paper, we study a class of parametric vector mixed quasivariational inequality problem of the Minty type (in short, (MQVIP)). Afterward, we establish some sufficient conditions for the stability properties such as the inner-openness, lower semicontinuity and Hausdorff lower semicontinuity of the solution mapping for this problem. The results presented in this paper is new and wide to the corresponding results in the literature


I—In a previous paper the present writer discussed both theoretically and experimentally the equilibrium and elastic stability of a thin twisted strip, and the results obtained by the theory were found to be in good agreement with observation. It has, however, been pointed out by Professor Southwell, F. R. S., that the solution of the stability equations which was given in that paper may only be regarded as an approximate solution for, although it satisfies exactly the differential equations and two boundary conditions along the edge of the strip, it only satisfies the two remaining boundary conditions approximately. The author has also noticed that the coefficients n a m in the Fourier expansion of θ 2 cos mθ which were used in A are incorrect when m = 0, and this has led to errors in the numerical work so that the values of ᴛb 2 / π 2 h which are given in Table I of A are wrong. In the present paper a solution of the stability equations is obtained which satisfies all the boundary conditions. This solution is very much more complicated than the approximate solution and much greater labour is required for the numerical work. The numerical work for the approximate solution of A has also been revised and the corrected results are given in 9, 10. It is found that the results for the approximate solution are in good agreement with those obtained from the exact solution and that both agree moderately well with the experimental results which are given in A. The main part of this paper is an extension of the previous work and is concerned with the stability of a thin twisted strip when it is subjected to a tension along its length. The theory has been compared with experiment and satisfactorily good agreement between them was found.


Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 384
Author(s):  
Janusz Brzdȩk ◽  
Zbigniew Leśniak ◽  
Renata Malejki

We study the Ulam-type stability of a generalization of the Fréchet functional equation. Our aim is to present a method that gives an estimate of the difference between approximate and exact solutions of this equation. The obtained estimate depends on the values of the coefficients of the equation and the form of the control function. In the proofs of the main results, we use a fixed point theorem to get an exact solution of the equation close to a given approximate solution.


2019 ◽  
Vol 35 (3) ◽  
pp. 393-406
Author(s):  
C. S. LALITHA ◽  
◽  

The main objective of this paper is to investigate the stability of solution sets of perturbed set optimization problems in the decision space as well as in the image space, by perturbing the objective maps. For a sequence of set-valued maps, a notion of gamma convergence is introduced to establish the external and internal stability in terms of Painlev´e–Kuratowski convergence of sequence of solution sets of perturbed problems under certain compactness assumptions and domination properties.


Author(s):  
Yongjin Li ◽  
Yan Shen

The aim of this paper is to prove the stability in the sense of Hyers-Ulam of differential equation of second ordery′′+p(x)y′+q(x)y+r(x)=0. That is, iffis an approximate solution of the equationy′′+p(x)y′+q(x)y+r(x)=0, then there exists an exact solution of the equation near tof.


2005 ◽  
Vol 8 (1) ◽  
pp. 60-62
Author(s):  
Dhuha Majeed Saleh ◽  
◽  
Abdul Samee A. Al-Janabi ◽  
M. K. Jasim ◽  
◽  
...  

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