期刊
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
卷 42, 期 5, 页码 2453-2480出版社
MALAYSIAN MATHEMATICAL SCIENCES SOC
DOI: 10.1007/s40840-018-0612-2
关键词
Weighted statistical convergence and weighted statistical summability; Fractional-order difference operators of functions; Relatively uniform convergence; The rates of convergence; Korovkin- and Voronovskaja-type approximation theorems
类别
In the present paper, we introduce the notion of relatively uniform weighted summability and its statistical version based upon fractional-order difference operators of functions. The concept of relatively uniform weighted alpha beta-statistical convergence is also introduced and some inclusion relations concerning the newly proposed methods are derived. As an application, we prove a general Korovkin-type approximation theorem for functions of two variables and also construct an illustrative example by the help of generating function type non-tensor Meyer-Konig and Zeller operators. Moreover, it is shown that the proposed methods are non-trivial generalizations of relatively uniform convergence which includes a scale function. We estimate the rate of convergence of approximating positive linear operators by means of the modulus of continuity and give a Voronovskaja-type approximation theorem. Finally, we present some computational results and geometrical interpretations to illustrate some of our approximation results.
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