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Sigma order continuity and best approximation in L ϱ -spaces

Shelby J. Kilmer, Wojciech M. Kozƚowski, Grzegorz Lewicki (1991)

Commentationes Mathematicae Universitatis Carolinae

In this paper we give a characterization of σ -order continuity of modular function spaces L ϱ in terms of the existence of best approximants by elements of order closed sublattices of L ϱ . We consider separately the case of Musielak–Orlicz spaces generated by non- σ -finite measures. Such spaces are not modular function spaces and the proofs require somewhat different methods.

Some common fixed point results for rational type contraction mappings in partially ordered metric spaces

Sumit Chandok (2013)

Mathematica Bohemica

The purpose of this paper is to establish some common fixed point results for f -nondecreasing mappings which satisfy some nonlinear contractions of rational type in the framework of metric spaces endowed with a partial order. Also, as a consequence, a result of integral type for such class of mappings is obtained. The proved results generalize and extend some of the results of J. Harjani, B. Lopez, K. Sadarangani (2010) and D. S. Jaggi (1977).

Strong unicity criterion in some space of operators

Grzegorz Lewicki (1993)

Commentationes Mathematicae Universitatis Carolinae

Let X be a finite dimensional Banach space and let Y ⊂ X be a hyperplane. Let L Y = { L ∈ L ( X , Y ) : L ∣ Y = 0 } . In this note, we present sufficient and necessary conditions on L 0 ∈ L Y being a strongly unique best approximation for given L ∈ L ( X ) . Next we apply this characterization to the case of X = l ∞ n and to generalization of Theorem I.1.3 from [12] (see also [13]).

Strong uniqueness.

Kroó, András, Pinkus, Allan (2010)

Surveys in Approximation Theory (SAT)[electronic only]

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