Abstract
Let be a non-negative matrix. Denote by , the infimum of those satisfying the following inequality:where , and is the Fibonacci numbers sequence and is a decreasing, non-negative sequence of real numbers. In this paper, first, the Fibonacci weighted sequence space is introduced. Then, we focus on the evaluation of , where is the Hausdorff matrix operator or the Nörlund matrix operator or the transpose of the Nörlund matrix operator. For the case of Hausdorff matrices, a Hardy-type formula is established as an upper estimate. Also, a general upper estimate is established for the case of Nörlund matrices and their transpose. In particular, we apply our results to Cesàro matrices, Hölder matrices, Euler matrices and Gamma matrices.
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