Functional equations and functional operator equations. A ℂ*-algebraic approach

2000 ◽  
pp. 25-116 ◽  
Author(s):  
A. B. Antonevich ◽  
A. V. Lebedev
Keyword(s):  
Functional Equations ◽  
Algebraic Approach ◽  
Operator Equations ◽  
Functional Operator

VOLTERRA FUNCTIONAL-OPERATOR EQUATIONS AND DISTRIBUTED OPTIMIZATION PROBLEMS

2018 ◽  
pp. 745-756
Author(s):  
Vladimir Iosifovich Sumin
Keyword(s):  
Optimization Problems ◽  
Initial Boundary ◽  
Optimization Methods ◽  
Global Solvability ◽  
Optimal Controls ◽  
Initial Boundary Value Problems ◽  
Operator Equations ◽  
Functional Operator ◽  
Controlled Systems ◽  
Initial Boundary Value

A survey of the results obtained in the theory of optimization of distributed systems by the method of Volterra functional-operator equations is given. Topics are considered: the conditions for preserving the global solvability of controllable initial-boundary value problems, optimality conditions, singular controlled systems in the sense of J.L. Lions, singular optimal controls, numerical optimization methods substantiation and others.

The solution existence and convergence analysis for linear and nonlinear differential-operator equations in Banach spaces within the Calogero type projection-algebraic scheme of discrete approximations

2009 ◽  
Vol 7 (4) ◽  
Author(s):  
Miroslaw Lustyk ◽  
Julian Janus ◽  
Marzenna Pytel-Kudela ◽  
Anatoliy Prykarpatsky
Keyword(s):  
Differential Operator ◽  
Banach Spaces ◽  
Linear Differential Operator ◽  
Algebraic Approach ◽  
Discrete Approximations ◽  
Operator Equations ◽  
Solution Convergence ◽  
Nonlinear Differential Operator ◽  
Linear And Nonlinear ◽  
Linear Differential

AbstractThe projection-algebraic approach of the Calogero type for discrete approximations of linear and nonlinear differential operator equations in Banach spaces is studied. The solution convergence and realizability properties of the related approximating schemes are analyzed. For the limiting-dense approximating scheme of linear differential operator equations a new convergence theorem is stated. In the case of nonlinear differential operator equations the effective convergence conditions for the approximated solution sets, based on a Leray-Schauder type fixed point theorem, are obtained.

On some functional equations related to derivations and bicircular projections in rings

2014 ◽  
Vol 49 (2) ◽  
pp. 313-331
Author(s):  
Maja Fošner ◽  
◽  
Benjamin Marcen ◽  
Nejc Širovnik ◽  
Joso Vukman ◽  
...  
Keyword(s):  
Functional Equations

Functional equations related to weightable quasi-metrics

2015 ◽  
Vol 4 (1047) ◽  
Author(s):  
M.J. Campion ◽  
E. Indurain ◽  
G. Ochoa
Keyword(s):  
Functional Equations

On Homogenization of Controlled Objects Described by Operator Equations of Hammerstein Type

2003 ◽  
Vol 35 (11) ◽  
pp. 19-27
Author(s):  
Victor N. Mizernyi ◽  
Peter I. Kogut ◽  
Tatyana N. Rudyanova
Keyword(s):  
Operator Equations
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