2015/08/24 by P. Nath, Prem Nath, Nath, P. +3
Computer Science · Mathematics · #Functional Equations Stability Results #cs.IT #math.IT #msc:39B52 #msc:39B82
paper · pdf · doi:10.48550/arxiv.1508.05910
18 pages. Already submitted for review
arxiv created 2015/08/24 · arxiv updated 2015/08/25
This paper is devoted to finding the general solutions of the functional equation \sumin \sumjm h(piqj)=\sumin h(pi)+\sumjm kj(qj)+λ\sumin h(pi)\sumjm kj(qj) valid for all complete probability distributions (p1,…,pn), (q1,…,qm), 0≤ pi≤ 1, 0≤ qj≤ 1, i=1,…,n; j=1,…,m, \sumin pi=1, \sumjm qj=1; n≥ 3, m≥ 3 fixed integers; λ∈\RR, λ≠ 0 and the mappings h:I→\RR, kj:I→\RR, j=1,…,m; I=[0,1], \RR denoting the set of all real numbers. A special case of the above functional equation was treated earlier by L. Losonczi and Gy. Maksa.