Journal of Nonlinear Sciences and Applications(JNSA)Journal of Nonlinear Sciences and ApplicationsJNSA 2008-1898 2008-1901International Scientific Research PublicationsJohor, Malaysiainfo@isr-publications.comisr-publications.comisr-publications.com/jnsa10.22436/jnsa.014.03.06On the stability of a sum form functional equation related to entropies of type ($$\alpha,\beta$$)SinghDhiraj Kumar
Department of Mathematics, Zakir Husain Delhi College (University of Delhi), Jawaharlal Nehru Marg, Delhi 110002, India
GroverShveta
Department of Mathematics, University of Delhi, Delhi 110007, India
In this paper, we discuss the stability of the sum form functional equation $\sum\limits _{i=1}^{n}\sum\limits _{j=1}^{m}f(p_{i} q_{j} ) =\sum\limits _{i=1}^{n}g(p_{i}) \sum\limits _{j=1}^{m}f(q_{j} )+\sum\limits _{i=1}^{n}f(p_{i}) \sum\limits _{j=1}^{m}q_{j}^{\beta }$ for all complete probability distributions $$(p_1,\ldots,p_n)\in \Gamma_n$$, $$(q_1,\ldots,q_m)\in \Gamma_m$$, $$n\ge 3$$, $$m\ge 3$$ are fixed integers, $$f$$, $$g$$ are real valued mappings each having the domain $$I=[0,1]$$ and $$\beta$$ is a fixed positive real power such that $$\beta \neq 1$$, $$0^\beta:=0$$, $$1^\beta:=1$$.
39B5239B82Stabilityadditive mappinglogarithmic mappingmultiplicative mappingbounded mappingentropies of type $$(\alpha,\beta)$$
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