On the general solutions of a system of functional equations on a commutative semigroup

1986 ◽  
Vol 17 (1) ◽  
pp. 27-35
Author(s):  
Z. Daróczy
Keyword(s):  
Commutative Semigroup ◽  
Functional Equations ◽  
System Of Functional Equations ◽  
General Solutions

scholarly journals Solution of Several Functional Equations on Nonunital Semigroups Using Wilson’s Functional Equations with Involution

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Jaeyoung Chung ◽  
Prasanna K. Sahoo
Keyword(s):  
Commutative Semigroup ◽  
Functional Equations ◽  
Complex Numbers ◽  
Commutative Semigroups ◽  
General Solutions

LetSbe a nonunital commutative semigroup,σ:S→San involution, andCthe set of complex numbers. In this paper, first we determine the general solutionsf,g:S→Cof Wilson’s generalizations of d’Alembert’s functional equations  fx+y+fx+σy=2f(x)g(y)andfx+y+fx+σy=2g(x)f(y)on nonunital commutative semigroups, and then using the solutions of these equations we solve a number of other functional equations on more general domains.

A SYSTEM OF FUNCTIONAL EQUATIONS SATISFIED BY COMPONENTS OF A QUADRATIC FUNCTION AND ITS STABILITY

2019 ◽  
Vol 100 (2) ◽  
pp. 304-316
Author(s):  
KANET PONPETCH ◽  
VICHIAN LAOHAKOSOL ◽  
SUKRAWAN MAVECHA
Keyword(s):  
Functional Equations ◽  
Quadratic Function ◽  
Stability Result ◽  
Circulant Matrix ◽  
System Of Functional Equations ◽  
General Solutions

A system of functional equations satisfied by the components of a quadratic function is derived via their corresponding circulant matrix. Given such a system of functional equations, general solutions are determined and a stability result for such a system is established.

MEASURES OF LOCAL ENTROPIES FOR COMPOSITIVE FUZZY PARTITIONS

2011 ◽  
Vol 19 (04) ◽  
pp. 717-728 ◽  
Author(s):  
DORETTA VIVONA ◽  
MARIA DIVARI
Keyword(s):  
Functional Equations ◽  
Fuzzy Measure ◽  
System Of Functional Equations ◽  
Locality Property ◽  
Fuzzy Measures ◽  
Fuzzy Partitions

The aim of this paper is to characterize of the measures of entropies without probability or fuzzy measure for compositive fuzzy partitions, taking into account the so-called locality property. We propose a system of functional equations, whose solutions give some forms of entropies without probability or fuzzy measures.

scholarly journals General Solutions of Two Quadratic Functional Equations of Pexider Type on Orthogonal Vectors

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Margherita Fochi
Keyword(s):  
Functional Equations ◽  
Inner Product ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Restricted Domain ◽  
Product Spaces ◽  
General Solutions ◽  
Inner Product Spaces ◽  
Restricted Domains

Based on the studies on the Hyers-Ulam stability and the orthogonal stability of some Pexider-quadratic functional equations, in this paper we find the general solutions of two quadratic functional equations of Pexider type. Both equations are studied in restricted domains: the first equation is studied on the restricted domain of the orthogonal vectors in the sense of Rätz, and the second equation is considered on the orthogonal vectors in the inner product spaces with the usual orthogonality.

scholarly journals Common Fixed Point Theorems in Metric Spaces with Applications

2018 ◽  
Vol 11 (4) ◽  
pp. 1177-1190
Author(s):  
Pushpendra Semwal
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
System Of Functional Equations ◽  
Contractive Type ◽  
Common Fixed Point Theorems

In this paper we investigate the existence and uniqueness of common fixed point theorems for certain contractive type of mappings. As an application the existence and uniqueness of common solutions for a system of functional equations arising in dynamic programming are discuss by using the our results.

ON A SYSTEM OF FUNCTIONAL EQUATIONS

1998 ◽  
Vol 31 (2) ◽  
Author(s):  
Nguyen Thanh Long ◽  
Nguyen Hoi Nghia ◽  
Nguyen Kim Khoi ◽  
Dinh Van Ruy
Keyword(s):  
Functional Equations ◽  
System Of Functional Equations
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