Sentence examples for a unique solution of the fixed from inspiring English sources

For each t in ( 0, 1 ), let x t denote a unique solution of the fixed point equation (2.2).

For each, let be a unique solution of the fixed-point equation.

This point x ¯ is also a unique solution of the mathematical programming with fixed point and split equilibrium constraints: min q ∈ Fix ( T ) ∩ Ω h ( q ).

This point x ¯ is also a unique solution of the mathematical programming with fixed point and split feasibility constraints: min q ∈ Fix ( T ) ∩ Ω h ( q ).

This point x ¯ is also a unique solution of the mathematical programming with fixed point and multiple sets split equilibrium constraints: min q ∈ Fix ( T ) ∩ Ω h ( q ).

This point x ¯ is also a unique solution of the mathematical programming with fixed point and multiple sets split feasibility constraints: min q ∈ Fix ( T ) ∩ Ω h ( q ).

This point x ¯ is also a unique solution of the mathematical programming problem with (MSSMVIP-1) and fixed point constraints: min x ∈ Fix ( T ) ∩ Ω 1 h ( x ).

This point x ¯ is also a unique solution of the following mathematical programming problem with (MSSMVIP-2) and fixed point constraints: min x ∈ Fix ( T ) ∩ Ω 2 h ( x ).

Hence, by the Banach fixed point theorem, we get that F has a fixed point which is a unique solution of the problem (1.1 - 1.2). □.

This point x ¯ is also a unique solution of the mathematical programming problem with (MSSMVIP-2) constraints: min x ∈ Fix ( T ) ∩ Ω 4 h ( x ).

where x ∗ = P Fix ( S ) f ( x ∗ ) is a unique solution of the variational inequality (3.1).