Polynomial Operators in Linear Spaces

2020 ◽  
pp. 339-419
Author(s):  
Ioannis K. Argyros
2018 ◽  
Vol 11 (4) ◽  
pp. 103-112
Author(s):  
Mahdi Iranmanesh ◽  
Maryam Saeedi Khojasteh

2012 ◽  
Vol 14 (2) ◽  
pp. 157
Author(s):  
Yanqiu WANG ◽  
Huaxin ZHAO
Keyword(s):  

2021 ◽  
pp. 108985
Author(s):  
Chun-Kit Lai ◽  
Bochen Liu ◽  
Hal Prince

Author(s):  
Anna Bahyrycz ◽  
Justyna Sikorska

AbstractLet X, Y be linear spaces over a field $${\mathbb {K}}$$ K . Assume that $$f :X^2\rightarrow Y$$ f : X 2 → Y satisfies the general linear equation with respect to the first and with respect to the second variables, that is, for all $$x,x_i,y,y_i \in X$$ x , x i , y , y i ∈ X and with $$a_i,\,b_i \in {\mathbb {K}}{\setminus } \{0\}$$ a i , b i ∈ K \ { 0 } , $$A_i,\,B_i \in {\mathbb {K}}$$ A i , B i ∈ K ($$i \in \{1,2\}$$ i ∈ { 1 , 2 } ). It is easy to see that such a function satisfies the functional equation for all $$x_i,y_i \in X$$ x i , y i ∈ X ($$i \in \{1,2\}$$ i ∈ { 1 , 2 } ), where $$C_1:=A_1B_1$$ C 1 : = A 1 B 1 , $$C_2:=A_1B_2$$ C 2 : = A 1 B 2 , $$C_3:=A_2B_1$$ C 3 : = A 2 B 1 , $$C_4:=A_2B_2$$ C 4 : = A 2 B 2 . We describe the form of solutions and study relations between $$(*)$$ ( ∗ ) and $$(**)$$ ( ∗ ∗ ) .


1991 ◽  
Vol 42 (3) ◽  
pp. 351-354 ◽  
Author(s):  
Sudarsan Nanda
Keyword(s):  

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