Positive definiteness of discrete quadratic functional

1997 ◽  
pp. 55-60 ◽  
Author(s):  
Martin Bohner
Keyword(s):  
Positive Definiteness ◽  
Quadratic Functional

scholarly journals POSITIVE SEMIDEFINITENESS OF DISCRETE QUADRATIC FUNCTIONALS

2003 ◽  
Vol 46 (3) ◽  
pp. 627-636 ◽  
Author(s):  
Martin Bohner ◽  
Ondřej Došlý ◽  
Werner Kratz
Keyword(s):  
Sufficient Conditions ◽  
Positive Definiteness ◽  
Quadratic Functional ◽  
Quadratic Functionals ◽  
Positive Semidefiniteness ◽  
Difference Systems ◽  
Special Cases ◽  
Even Order ◽  
Sturm Liouville ◽  
Necessary And Sufficient

AbstractWe consider symplectic difference systems, which contain as special cases linear Hamiltonian difference systems and Sturm–Liouville difference equations of any even order. An associated discrete quadratic functional is important in discrete variational analysis, and while its positive definiteness has been characterized and is well understood, a characterization of its positive semidefiniteness remained an open problem. In this paper we present the solution to this problem and offer necessary and sufficient conditions for such discrete quadratic functionals to be non-negative definite.AMS 2000 Mathematics subject classification: Primary 39A12; 39A13. Secondary 34B24; 49K99

scholarly journals Stability of a generalized n-variable mixed-type functional equation in fuzzy modular spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Murali Ramdoss ◽  
Divyakumari Pachaiyappan ◽  
Choonkil Park ◽  
Jung Rye Lee
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Research Paper ◽  
Fixed Point Method ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Modular Spaces

AbstractThis research paper deals with general solution and the Hyers–Ulam stability of a new generalized n-variable mixed type of additive and quadratic functional equations in fuzzy modular spaces by using the fixed point method.

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