HLAWKA’S FUNCTIONAL INEQUALITY ON TOPOLOGICAL GROUPS

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FECHNER WLODZIMIERZ

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Journal Paper

Paper Information

Journal: BANACH JOURNAL OF MATHEMATICAL ANALYSIS Year:2017 | Volume:11 | Issue:1 Page(s): 130-142

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Title

HLAWKA’S FUNCTIONAL INEQUALITY ON TOPOLOGICAL GROUPS

Author(s)

FECHNER WLODZIMIERZ | Issue Writer Certificate

Keywords

FUNCTIONAL INEQUALITY

HLAWKA’S INEQUALITY

DRYGAS INEQUALITY

SUBQUADRATIC MAPPING

Abstract

Let (X,+)(X,+) be a topological abelian group. We discuss regularity of solutions f:X®Rf:X®R of Hlawka’s functional inequality f(x+y)+f(y+z)+f(x+z)£f(x+y+z)+f(x)+f(y)+f(z),f(x+y)+f(y+z)+f(x+z)≤f(x+y+z)+f(x)+f(y)+f(z), postulated for all x,y,z∈Xx,y,z∈X. We study the lower and upper hull of ff. Moreover, we provide conditions which imply continuity of ff. We prove, in particular, that if XX is generated by any neighborhood of zero, f is continuous at zero, and f(0)=0f(0)=0, then f is continuous on X.

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APA: Copy

FECHNER, WLODZIMIERZ. (2017). HLAWKA’S FUNCTIONAL INEQUALITY ON TOPOLOGICAL GROUPS. BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 11(1), 130-142. SID. https://sid.ir/paper/317068/en

Vancouver: Copy

FECHNER WLODZIMIERZ. HLAWKA’S FUNCTIONAL INEQUALITY ON TOPOLOGICAL GROUPS. BANACH JOURNAL OF MATHEMATICAL ANALYSIS[Internet]. 2017;11(1):130-142. Available from: https://sid.ir/paper/317068/en

IEEE: Copy

WLODZIMIERZ FECHNER, “HLAWKA’S FUNCTIONAL INEQUALITY ON TOPOLOGICAL GROUPS,” BANACH JOURNAL OF MATHEMATICAL ANALYSIS, vol. 11, no. 1, pp. 130–142, 2017, [Online]. Available: https://sid.ir/paper/317068/en

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