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Abstract  

Recently P. Mache and M. W. Müller introduced the Baskakov quasi-interpolants and obtained an approximation equivalence theorem. In this paper we consider simultaneous approximation equivalence theorem for Baskakov quasi-interpolants.

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In the global navigation satellite system (GNSS) carrier phase data processing, cycle slips are limiting factors and affect the quality of the estimators in general. When differencing phase observations, a problem in phase ambiguity parameterization may arise, namely linear relations between some of the parameters. These linear relations must be considered as additional constraints in the system of observation equations. Neglecting these constraints, results in poorer estimators. This becomes significant when ambiguity resolution is in demand. As a clue to detect the problem in GNSS processing, we focused on the equivalence of using undifferenced and differenced observation equations. With differenced observables this equivalence is preserved only if we add certain constraints, which formulate the linear relations between some of the ambiguity parameters, to the differenced observation equations. To show the necessity of the additional constraints, an example is made using real data of a permanent station from the network of the international GNSS service (IGS). The achieved results are notable to the GNSS software developers.

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Abstract  

P. L. Ul'yanov has recently proved a new type of equivalence theorems in connection with the classical equivalence theorem by A. Plessner. Making use of certain results proved by us more than thirty years ago, we extend Ul'yanov's results into more general equivalence theorems.

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Abstract  

Among others a general equivalence theorem on Fourier cosine series with monotone coefficients are generalized to coefficients of rest bounded variation. Similarly some theorems of Aljančić are also extended, namely one of them in this generalized form is required to the proof of the equivalence theorem.

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Abstract  

Recently Müller [6] introduced the left Gamma quasi-interpolants and obtained an approximation equivalence theorem for them. We show the strong converse inequality of type B for the left Gamma quasi-interpolants.

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In this paper we give the direct, inverse and equivalence theorems for generalization Meyer-König and Zeller type operators in the space L p (1 ≦ p ) with Ditzian-Totik modulus.

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Abstract  

We present an equivalence theorem, which includes all known characterizations of the class B p, i.e., the weight class of Ariño and Muckenhoupt, and also some new equivalent characterizations. We also give equivalent characterizations for the classes B p *, B * and RB p, and prove and apply a “gluing lemma” of independent interest.

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