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In this work, vector-valued continuous functions are approximated uniformly on the unit hypercube by Shepard operators. If lambda denotes the usual parameter of the Shepard operators and m is the dimension of the hypercube, then our results show that it is possible to obtain a uniform approximation of a continuous vector-valued function by these operators when lambda >= m+1. By using three-dimensional parametric plots, we illustrate this uniform approximation for some vector-valued functions. Finally, the influence in approximation by regular summability processes is studied, and their motivation is shown.

In the present work, in order to approximate integrable vector-valued functions, we study the Kantorovich version of vector-valued Shepard operators. We also display some applications supporting our results by using parametric plots of a surface and a space curve. Finally, we also investigate how nonnegative regular (matrix) summability methods affect the approximation.

In this paper, by using multivariable Taylor polynomials and also the max-product operation, we give a nonlinear modification of the classical Shepard operators. This modification enables us to obtain better approximation behavior than the classical aspects studied by Shepard (1968) and Farwig (1986). We also discuss the effects of regular summability methods in the approximation. At the end of the paper, we give some applications and graphical simulations verifying our approximation results.; COPY; 2023 Elsevier B.V. All rights reserved.

In this work, using regular integral transformations on time scales, we generalize the concept of statistical convergence. This enables us not only to unify discrete and continuous cases known in the literature but also to derive new convergence methods with choices of appropriate transformations and time scales. This is a continuation of our earlier work and includes many new methods. We obtain sufficient conditions for regularity of kernel functions on time scales and also we prove a characterization theorem for the generalized statistical convergence. At the end of the paper we display some applications and special cases of our results.

In this work, using regular integral transformations on time scales, we generalize the concept of statistical convergence. This enables us not only to unify discrete and continuous cases known in the literature but also to derive new convergence methods with choices of appropriate transformations and time scales. This is a continuation of our earlier work and includes many new methods. We obtain sufficient conditions for regularity of kernel functions on time scales and also we prove a characterization theorem for the generalized statistical convergence. At the end of the paper we display some applications and special cases of our results.

We first construct a sequence of double smooth Picard singular integral operators which do not have to be positive in general. After giving some useful estimates, we mainly show that it is possible to approximate a function by these operators in statistical sense even though they do not obey the positivity condition of the statistical Korovkin theory., Scientific and Technological Research Council of Turkey (TUBITAK) [108T229], The second author was partially supported by the Scientific and Technological Research Council of Turkey (TUBITAK); Project No: 108T229.

X bir Haussdorf uzayı ve (X,U) bir düzgün yapı olsun. F, X üzerinde tanımlı reel değerli fonksiyonlardan oluşan bir vektör uzay olsun ve sabit fonksiyonları içersin. Ayrıca kabul edelim ki Y uzayı X uzayının kompakt bir alt uzayı ve {L_n} , F den R^Y ye tanımlı pozitif lineer operatörlerin bir dizisi olsun. Bu yüksek lisans tezinde istatistiksel Korovkin tipi yaklaşım teoremleri elde ettik. Daha sonra elde ettiğimiz teoremlerin önemli uygulamaları üzerinde durularak elde ettiğimiz yaklaşım sonuçlarımızın klasik teoremlerden daha güçlü ve uygulanabilir olduğunu gösterdik. Üstelik sonuçlarımızı çok değişkenli fonksiyon uzaylarına da genelleştirdik.Let X be a Haussdorff space provided with the uniform structure (X,U). Let F be a vector space of real-valued functions defined on X including the constant-valued functions, Assume further that Y is a compact subspace of X and that {L_n} is a sequence of positive linear operators of F into R^Y. In this thesis, we obtain an abstract Korovkin-type approximation theorem in statistical sense. Then, by displaying some significant applications, we show that our approximation is more applicable and powerful than the classical ones. Furthermore, we extend our results to the multivariate function spaces.

In this paper, we introduce the Kantorovich version of complex Shepard operators in order to approximate functions whose pth powers are integrable on the unit square. We also give an application which explains why we need such operators. Furthermore, we study the effects of some regular summability methods on this Lp-approximation. © 2022 Elsevier Inc., The authors would like to thank the referee for providing insightful comments and reading the manuscript carefully.

Let (Y-n) be a sequence of random variables whose probability distributions depend on x is an element of [a, b]. It is well-known that if {E (Y-n - x)(2)} converges uniformly to zero on [a, b], then, for all f is an element of C[a, b], {E (f (Y-n))1 is uniformly convergent to f on [a, b], where E denotes the mathematical expectation. In this paper, we mainly improve this result via the concept of statistical convergence from the summability theory, which is a weaker method than the usual convergence. Furthermore, we construct an example such that our new result is applicable while the classical one is not.

Bu tezde, zaman skalaları üzerinde tanımlanan reel değerli ve ?-ölçülebilir fonksiyonların istatistiksel yakınsaklığı kavramı incelenmiş ve bu yakınsaklık metodu için çeşitli karakterizasyonlar elde edilmiştir. Bu çalışmada elde ettiğimizsonuçlar literatürde var olan istatistiksel yakınsaklık metotlarını içermenin yanı sıra, bir çok yeni metot için de uygulama alanı oluşturmaktadır.Bu tez dört bölümden oluşmaktadır. İlk bölüm giriş kısmına ayrılmıştır. İkinci bölümde zaman skalası teorisine ve istatistiksel yakınsaklığa ilişkin temel tanımve teoremlere yer verilmiştir. Orjinal sonuçlarımızın bulunduğu üçüncü bölümde, bir zaman skalası üzerinde tanımlanan fonksiyonun istatistiksel yakınsaklığı inşaedilmiş ve hangi koşullar altnda bu yakınsamanın gerçeklendiği araştırılmıştır.Son bölümde ise bu tezden elde edilen çıktılara ve gelecekte konuyla ilgili dahanelerin yapılabileceğine değinilmiştir., In this thesis, we investigate the statistical convergence of real-valued and ?-measurable functions defined on time scales and we obtain some characterizations for this convergence method. Our results obtained in this study not only includethe previous statistical convergence methods in the literature but also enable some aplication areas for various new methods.This thesis consists of four chapters. The first chapter is devoted to the introduction. In the second chapter, we recall some basic denitions and theorems regarding the theory of time scales and statistical convergence. In the thirdchapter that includes our original results, we construct the statistical convergence of a function defined on a time scale and investigate under which conditions this convergence holds. In the last chapter, we discuss the outputs of the thesis andthe future projects improving this topic.

In this paper, by using nonnegative regular summability methods we improve and generalize the approximation properties of max-min operators which have been investigated systematically in our recent paper published in 2020 in this journal. We also discuss the rate of convergence in the approximation. Applications and concluding remarks at the end of the paper explain why we need such summability methods. (c) 2021 Elsevier B.V. All rights reserved.

We first construct a sequence of double smooth Picard singular integral operators which do not have to be positive in general. After giving some useful estimates, we mainly show that it is possible to approximate a function by these operators in statistical sense even though they do not obey the positivity condition of the statistical Korovkin theory., Scientific and Technological Research Council of Turkey (TUBITAK) [108T229], The second author was partially supported by the Scientific and Technological Research Council of Turkey (TUBITAK); Project No: 108T229.