General Solution of a Functional Equation Connected with a Characterization of Statistical Distributions

1975 ◽  
pp. 47-55 ◽  
Author(s):  
J. Aczél
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Statistical Distributions

scholarly journals On the general solution of a functional equation connected to sum form information measures on open domain—III

1986 ◽  
Vol 9 (3) ◽  
pp. 545-550 ◽  
Author(s):  
Pl. Kannappan ◽  
P. K. Sahoo
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Open Domain ◽  
Information Measures ◽  
Domain Iii ◽  
Weighted Entropy ◽  
Form Information

In this series, this paper is devoted to the study of a functional equation connected with the characterization of weighted entropy and weighted entropy of degreeβ. Here, we find the general solution of the functional equation (2) on an open domain, without using0-probability and1-probability.

scholarly journals Characterization of t-affine differences and related forms

2021 ◽  
Author(s):  
Andrzej Olbryś
Keyword(s):  
Functional Equation ◽  
General Solution

AbstractIn the present paper we are concerned with the problem of characterization of maps which can be expressed as an affine difference i.e. a map of the form $$\begin{aligned} tf(x)+(1-t)f(y)-f(tx+(1-t)y), \end{aligned}$$ t f ( x ) + ( 1 - t ) f ( y ) - f ( t x + ( 1 - t ) y ) , where $$t\in (0,1)$$ t ∈ ( 0 , 1 ) is a given number. We give a general solution of the functional equation associated with this problem.

scholarly journals On a conditional Cauchy functional equation of several variables and a characterization of multivariate stable distributions

1993 ◽  
Vol 16 (1) ◽  
pp. 165-168 ◽  
Author(s):  
Arjun K. Gupta ◽  
Truc T. Nguyen ◽  
Wei-Bin Zeng
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Stable Distributions ◽  
Cauchy Functional Equation ◽  
Several Variables

The general solution of a conditional Cauchy functional equation of several variables is obtained and its applications to the characterizations of multivariate stable distributions are studied.

Solutions and Stability of Generalized Mixed Type QCA-Functional Equations in Random Normed Spaces

2013 ◽  
Vol 59 (2) ◽  
pp. 299-320
Author(s):  
M. Eshaghi Gordji ◽  
Y.J. Cho ◽  
H. Khodaei ◽  
M. Ghanifard
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Probabilistic Normed Spaces ◽  
Random Normed Spaces ◽  
Generalized Stability

Abstract In this paper, we investigate the general solution and the generalized stability for the quartic, cubic and additive functional equation (briefly, QCA-functional equation) for any k∈ℤ-{0,±1} in Menger probabilistic normed spaces.

A fixed point approach to the stability of sextic Lie *-derivations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4933-4944
Author(s):  
Dongseung Kang ◽  
Heejeong Koh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Single Case ◽  
Fixed Point Method ◽  
Point Method ◽  
Fixed Point Approach ◽  
The Stability ◽  
The Given ◽  
Lie Derivations

We obtain a general solution of the sextic functional equation f (ax+by)+ f (ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)] + 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.

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.

scholarly journals Solution and Stability of a Mixed Type Cubic and Quartic Functional Equation in Quasi-Banach Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
S. Zolfaghari ◽  
J. M. Rassias ◽  
M. B. Savadkouhi
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Banach Spaces ◽  
Mixed Type ◽  
Quartic Functional Equation

We obtain the general solution and the generalized Ulam-Hyers stability of the mixed type cubic and quartic functional equationf(x+2y)+f(x−2y)=4(f(x+y)+f(x−y))−24f(y)−6f(x)+3f(2y)in quasi-Banach spaces.

scholarly journals Stability of a Functional Equation Deriving from Quadratic and Additive Functions in Non-Archimedean Normed Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Abasalt Bodaghi ◽  
Sang Og Kim
Keyword(s):  
Functional Equation ◽  
Positive Integer ◽  
General Solution ◽  
Functional Equations ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Additive Functions ◽  
Normed Spaces

We obtain the general solution of the generalized mixed additive and quadratic functional equationfx+my+fx−my=2fx−2m2fy+m2f2y,mis even;fx+y+fx−y−2m2−1fy+m2−1f2y,mis odd, for a positive integerm. We establish the Hyers-Ulam stability for these functional equations in non-Archimedean normed spaces whenmis an even positive integer orm=3.

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