ON HYPERSTABILITY OF GENERALIZED LINEAR EQUATIONS IN SEVERAL VARIABLES IN QUASI-NORMED SPACES

2020 ◽  
Vol 9 (5) ◽  
pp. 33-41
Author(s):  
Quy Nguyen Phu ◽  
Dung Nguyen Van
Keyword(s):  
Linear Equations ◽  
Normed Spaces ◽  
Several Variables

HYPERSTABILITY OF GENERALISED LINEAR FUNCTIONAL EQUATIONS IN SEVERAL VARIABLES

2020 ◽  
Vol 102 (2) ◽  
pp. 293-302
Author(s):  
THEERAYOOT PHOCHAI ◽  
SATIT SAEJUNG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Functional Equations ◽  
Linear Functional ◽  
Linear Equations ◽  
General Linear ◽  
Several Variables ◽  
Linear Functional Equations

Zhang [‘On hyperstability of generalised linear functional equations in several variables’, Bull. Aust. Math. Soc.92 (2015), 259–267] proved a hyperstability result for generalised linear functional equations in several variables by using Brzdęk’s fixed point theorem. We complete and extend Zhang’s result. We illustrate our results for general linear equations in two variables and Fréchet equations.

scholarly journals Generalisation of the Frobenius Formula in the Theory of Block Operators on Normed Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3066
Author(s):  
Nikolai A. Sidorov ◽  
Aliona I. Dreglea ◽  
Denis N. Sidorov
Keyword(s):  
Essential Role ◽  
Laurent Series ◽  
Existence Theorems ◽  
Linear Equations ◽  
Asymptotic Approximations ◽  
System Of Linear Equations ◽  
Normed Spaces ◽  
Integrodifferential System ◽  
Block Operator ◽  
Efficient Construction

The efficient construction and employment of block operators are vital for contemporary computing, playing an essential role in various applications. In this paper, we prove a generalisation of the Frobenius formula in the setting of the theory of block operators on normed spaces. A system of linear equations with the block operator acting in Banach spaces is considered. Existence theorems are proved, and asymptotic approximations of solutions in regular and irregular cases are constructed. In the latter case, the solution is constructed in the form of a Laurent series. The theoretical approach is illustrated with an example, the construction of solutions for a block equation leading to a method of solving some linear integrodifferential system.

The Effects of Fluid Entry Conditions on the Performance of Vapour-Jet Compressors

1978 ◽  
Vol 5 (1) ◽  
pp. 9-14 ◽  
Author(s):  
N. Galanis ◽  
G. Faucher ◽  
Nguyen Mau Phung
Keyword(s):  
Experimental Data ◽  
Numerical Solution ◽  
Linear Equations ◽  
Gas Analysis ◽  
Phase Changes ◽  
Perfect Gas ◽  
Expansion Process ◽  
One Dimensional ◽  
Several Variables ◽  
Non Linear Equations

An earlier one-dimensional frictionless perfect-gas analysis of jet ejectors is generalized to account for phase changes during the expansion process and is used to evaluate the performance of vapour-jet compressors operating with initially saturated freon-12 or n-butane. The results, obtained by numerical solution of the non-linear equations, show better agreement with experimental data than the predictions based on perfect-gas relations and indicate that the performance depends upon several variables which are not accounted for by the perfect-gas model.

scholarly journals Linear equations over multiplicative groups, recurrences, and mixing III

2017 ◽  
Vol 38 (7) ◽  
pp. 2625-2643 ◽  
Author(s):  
H. DERKSEN ◽  
D. MASSER
Keyword(s):  
Prime Ideal ◽  
Equivalence Relation ◽  
Linear Equations ◽  
Several Variables ◽  
Natural Equivalence ◽  
Ring Of Polynomials ◽  
Multiplicative Groups

Given an algebraic $\mathbf{Z}^{d}$-action corresponding to a prime ideal of a Laurent ring of polynomials in several variables, we show how to find the smallest order $n+1$ of non-mixing. It is known that this is determined by the non-mixing sets of size $n+1$, and we show how to find these in an effective way. When the underlying characteristic is positive and $n\geq 2$, we prove that there are at most finitely many classes under a natural equivalence relation. We work out two examples, the first with five classes and the second with 134 classes.

scholarly journals Using Linear Equations Approach to Formulate Balanced and Least-Cost Ration for Dairy Cattl

2021 ◽  
Vol 910 (1) ◽  
pp. 012089
Author(s):  
Sary Mahir Ailia Shaawi ◽  
Noor Ezat Jalil Astefan
Keyword(s):  
Wheat Bran ◽  
Soybean Meal ◽  
Crude Protein ◽  
Linear Equations ◽  
Metabolizable Energy ◽  
Microsoft Excel ◽  
Protein Ratio ◽  
Several Variables ◽  
Mathematical Formulas ◽  
The Cost

Abstract The main objective of this study was to find an effective way to use linear equations for the purpose of creating a balanced ration at the lowest possible cost for dairy cattle by using linear equations and solving these equations through the Solver tool provided by MS-Excel. Samples of barley, corn, wheat bran, soybean meal and wheat straw were collected from the local markets and the necessary chemical analyzes were performed for them. after that the mathematical formulas of the linear equations were developed according to the specified constraints for crude protein ratio, value of metabolizable energy and the percentage of each calcium and phosphorus, which meets the needs of a medium-production dairy cow (15 kg) and weighting (650 kg). then the data was entered into Microsoft Excel and the equations were solved by Solver tool. The results showed a superior ability of linear equations to solve the problems consisting of several variables where the feed was formed by mixing barley, Corn, wheat bran, soybean meal, wheat hay, calcium phosphate and salt in proportions ( 5, 17.91, 50, 10.76, 13.66, 1.64 and 1) respectively, The cost of the feed mixture was (268.6 $/ton), which is the lowest possible cost for a ration that meets the required needs, linear programming will provide the animal breeders efficiency with the highest production by reducing the costs and balancing of the ration through the steps described in the search.

scholarly journals Equalities and inequalities for several variables mappings

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Abasalt Bodaghi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Single Equation ◽  
Ulam Stability ◽  
Systems Of Equations ◽  
Normed Spaces ◽  
Mild Conditions ◽  
Several Variables

AbstractIn this paper, some special mappings of several variables such as the multicubic and the multimixed quadratic–cubic mappings are introduced. Then, the systems of equations defining a multicubic and a multimixed quadratic–cubic mapping are unified to a single equation. Under some mild conditions, it is shown that a multimixed quadratic–cubic mapping can be multiquadratic, multicubic and multiquadratic–cubic. Furthermore, by applying a known fixed-point theorem, the Hyers–Ulam stability of multimixed quadratic–cubic, multiquadratic, multicubic and multiquadratic–cubic are studied in non-Archimedean normed spaces.

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