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.
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.
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.
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.
Authors:Shunsheng Guo, Lixia Liu, Qiulan Qi, and Gengsheng Zhang
Recently Müller  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.
Authors:A. Gogatishvili, A. Kufner, and L. Persson
We present an equivalence theorem, which includes all known characterizations of the class Bp, i.e., the weight class of Ariño and Muckenhoupt, and also some new equivalent characterizations. We also give equivalent
characterizations for the classes Bp*, B∞* and RBp, and prove and apply a “gluing lemma” of independent interest.