We study bounded positive definite double sequences which are stationary with respect to a polynomial hypergroup structure generated by (Rn(t)) ∈nNo. Connected with bounded positive definite and Rn-stationary double sequences is an Rn-stationary sequence of elements in a Hilbert space. We derive an ergodic theorem for such Rn-stationary sequences and we give a complete characterization of the space of multipliers defined by such an Rn-stationary sequence. Further we give examples of bounded positive definite double sequences.
Some developments of the second-order characterizations of convex functions are investigated by using the coderivative of the subdifferential mapping. Furthermore, some applications of the second-order subdifferentials in optimization problems are studied.
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