Continuity of ?-subgradient mappings

Cybernetics ◽  
1978 ◽  
Vol 13 (5) ◽  
pp. 790-791 ◽  
Author(s):  
E. A. Nurminskii
Keyword(s):  
Subgradient Mappings

Variational conditions and the proto-differentiation of partial subgradient mappings

1996 ◽  
Vol 26 (12) ◽  
pp. 1951-1964 ◽  
Author(s):  
A.B Levy ◽  
R.T. Rockafellar
Keyword(s):  
Subgradient Mappings

scholarly journals A General Class of Differential Hemivariational Inequalities Systems in Reflexive Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3173
Author(s):  
Lu-Chuan Ceng ◽  
Ching-Feng Wen ◽  
Yeong-Cheng Liou ◽  
Jen-Chih Yao
Keyword(s):  
Evolution Equations ◽  
Recent Literature ◽  
Type System ◽  
Parabolic Type ◽  
Hemivariational Inequalities ◽  
Product Spaces ◽  
Reflexive Banach Spaces ◽  
Evolution Triple ◽  
Iterative System ◽  
Subgradient Mappings

We consider an abstract system consisting of the parabolic-type system of hemivariational inequalities (SHVI) along with the nonlinear system of evolution equations in the frame of the evolution triple of product spaces, which is called a system of differential hemivariational inequalities (SDHVI). A hybrid iterative system is proposed via the temporality semidiscrete technique on the basis of the Rothe rule and feedback iteration approach. Using the surjective theorem for pseudomonotonicity mappings and properties of the partial Clarke’s generalized subgradient mappings, we establish the existence and priori estimations for solutions to the approximate problem. Whenever studying the parabolic-type SHVI, the surjective theorem for pseudomonotonicity mappings, instead of the KKM theorems exploited by other authors in recent literature for a SHVI, guarantees the successful continuation of our demonstration. This overcomes the drawback of the KKM-based approach. Finally, via the limitation process for solutions to the hybrid iterative system, we derive the solvability of the SDHVI with no convexity of functions u↦fl(t,x,u),l=1,2 and no compact property of C0-semigroups eAl(t),l=1,2.

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