scholarly journals Hölder Continuity of a Parametric Generalized Variational Inequality

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Li-na Wang ◽  
Xiao-bing Li
Keyword(s):  
Variational Inequality ◽  
Projection Method ◽  
Hölder Continuity ◽  
Sufficient Conditions ◽  
Metric Projection ◽  
Holder Continuity ◽  
Data Perturbation ◽  
Generalized Variational Inequality ◽  
Solution Mapping

By using the classic metric projection method, we obtain sufficient conditions for Hölder continuity of the nonunique solution mapping for a parametric generalized variational inequality with respect to data perturbation. The result is different from the recent ones in the literature and has a strong geometric flavor.

scholarly journals Hölder Continuity of Solutions to Parametric Generalized Vector Quasiequilibrium Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Z. Y. Peng
Keyword(s):  
Recent Literature ◽  
Hölder Continuity ◽  
Sufficient Conditions ◽  
Holder Continuity ◽  
Quasiequilibrium Problems ◽  
Scalarization Method ◽  
Set Valued Mappings ◽  
Vector Quasiequilibrium Problems ◽  
Quasiequilibrium Problem ◽  
Vector Quasiequilibrium Problem

By using a linear scalarization method, we establish sufficient conditions for the Hölder continuity of the solution mappings to a parametric generalized vector quasiequilibrium problem with set-valued mappings. These results extend the recent ones in the recent literature, (e.g., Li et al. (2009), Li et al. (2011)). Furthermore, two examples are given to illustrate the obtained result.

scholarly journals Stability analysis of solutions to equilibrium problems and applications in economics

2020 ◽  
Vol 4 (3) ◽  
pp. 121-132
Author(s):  
Tran Ngoc Tam ◽  
Nguyen Minh Hai ◽  
Bantaojai Thanatporn
Keyword(s):  
Stability Analysis ◽  
Design Methodology ◽  
Equilibrium Problems ◽  
Hölder Continuity ◽  
Sufficient Conditions ◽  
Strong Convexity ◽  
Holder Continuity ◽  
Content Type ◽  
Solution Maps

Purpose The purpose of this paper is to study the Hölder calmness of solutions to equilibrium problems and apply it to economics. Design/methodology/approach The authors obtain the Hölder calmness by using an effective approach. More precisely, under the key assumption of strong convexity, sufficient conditions for the Hölder continuity of solution maps to equilibrium problems are established. Findings A new result in stability analysis for equilibrium problems and applications in economics is archived. Originality/value The authors confirm that the paper has not been published previously, is not under consideration for publication elsewhere and is not being simultaneously submitted elsewhere.

On nonhomeomorphic mappings with the inverse Poletsky inequality

2020 ◽  
Vol 17 (3) ◽  
pp. 414-436
Author(s):  
Evgeny Sevost'yanov ◽  
Serhii Skvortsov ◽  
Oleksandr Dovhopiatyi
Keyword(s):  
Boundary Behavior ◽  
Hölder Continuity ◽  
Continuous Extension ◽  
Quasiconformal Mappings ◽  
Holder Continuity ◽  
Hölder Continuous ◽  
Finite Distortion ◽  
Mappings Of Finite Distortion ◽  
Lipschitz Continuous ◽  
Inverse Inequality

As known, the modulus method is one of the most powerful research tools in the theory of mappings. Distortion of modulus has an important role in the study of conformal and quasiconformal mappings, mappings with bounded and finite distortion, mappings with finite length distortion, etc. In particular, an important fact is the lower distortion of the modulus under mappings. Such relations are called inverse Poletsky inequalities and are one of the main objects of our study. The use of these inequalities is fully justified by the fact that the inverse inequality of Poletsky is a direct (upper) inequality for the inverse mappings, if there exist. If the mapping has a bounded distortion, then the corresponding majorant in inverse Poletsky inequality is equal to the product of the maximum multiplicity of the mapping on its dilatation. For more general classes of mappings, a similar majorant is equal to the sum of the values of outer dilatations over all preimages of the fixed point. It the class of quasiconformal mappings there is no significance between the inverse and direct inequalities of Poletsky, since the upper distortion of the modulus implies the corresponding below distortion and vice versa. The situation significantly changes for mappings with unbounded characteristics, for which the corresponding fact does not hold. The most important case investigated in this paper refers to the situation when the mappings have an unbounded dilatation. The article investigates the local and boundary behavior of mappings with branching that satisfy the inverse inequality of Poletsky with some integrable majorant. It is proved that mappings of this type are logarithmically Holder continuous at each inner point of the domain. Note that the Holder continuity is slightly weaker than the classical Holder continuity, which holds for quasiconformal mappings. Simple examples show that mappings of finite distortion are not Lipschitz continuous even under bounded dilatation. Another subject of research of the article is boundary behavior of mappings. In particular, a continuous extension of the mappings with the inverse Poletsky inequality is obtained. In addition, we obtained the conditions under which the families of these mappings are equicontinuous inside and at the boundary of the domain. Several cases are considered: when the preimage of a fixed continuum under mappings is separated from the boundary, and when the mappings satisfy normalization conditions. The text contains a significant number of examples that demonstrate the novelty and content of the results. In particular, examples of mappings with branching that satisfy the inverse Poletsky inequality, have unbounded characteristics, and for which the statements of the basic theorems are satisfied, are given.

scholarly journals Linearization and Hölder continuity for nonautonomous systems

2021 ◽  
Vol 297 ◽  
pp. 536-574
Author(s):  
Lucas Backes ◽  
Davor Dragičević ◽  
Kenneth J. Palmer
Keyword(s):  
Hölder Continuity ◽  
Holder Continuity ◽  
Nonautonomous Systems
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