- Conference date: 7–12 June 2009
- Location: Sozopol (Bulgaria)
In this paper, inequalities for convex combinations of functionals satisfying the condition /a/ and /b/, formulated in the theorems and suggestions are proved. The condition /a/ relates to non‐negative functionals about which the inequalities Theorem.1 and Theorem.2 seminorned are proved. In Theorem.1 we consider seminorned spaces and in Theorem.2—seminormed algebras. The condition Pol relates generally to representations between seminormed spaces and seminormed algebras. The inequalities formulated in this way are proved in Sggestion.1 and Suggestion.2. For the first time in this article we consider the following generalization of the convexity in a seminormed algebras where ‖.‖ is the norm in A, and γ is a real number.
A point of departure about the received results are analogous inequalities /like the inequality in Example/, related to real functionals of one variable. They had been used in the geometry of the banach spaces Similar statements related to functionals in finite dimensional spaces and countable dimensional spaces are made in These results can be applied in the mentioned areas.
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