İsmail Aslan

Verified

İsmail verified their affiliation via an institutional email.

Learn more

Verified

İsmail verified their affiliation via an institutional email.

Learn more

• Doctor of Philosophy
• Professor (Associate) at Hacettepe University

This project will address the applications of artificial neural network operators in approximation theory and morphological image processing. As is known, Cardaliagnet and Euvrard proposed an approach using neural networks to approximate a function in 1992. These operators, referred to as neural network operators in the literature, preserved the ap...

In this paper, we introduce a max-min approach for approximation by neural network operators activated by sigmoidal functions. Our focus lies in addressing both pointwise and uniform convergence in the context of univariate functions. Then, we investigate the order of approximation. We also take into account the max-min quasi-interpolation operator...

In this study, considering the well-known fractal image compression, we introduce the image decompression method through non-affine contraction mappings. To achieve this, we convert affine contraction mappings into non-affine contraction mappings using Lipschitz continuous functions, subject to certain assumptions. Our expectation is to obtain deco...

In this paper, we explore $N$-dimensional nonlinear discrete operators, closely related to generalized sampling series. We investigate their approximation properties by using the supremum norm and employ a summability method to generalize the discrete operators. The order of convergence is studied by using suitable Lipschitz classes of uniformly co...

In this work, we study the Kantorovich variant of max-min neural network operators, in which the operator kernel is defined in terms of sigmoidal functions. Our main aim is to demonstrate the $L^{p}$-convergence of these nonlinear operators for $1\leq p<\infty$, which makes it possible to obtain approximation results for functions that are not nece...

In the present paper, we examine Mellin-type nonlinear integral operators equipped with the Haar measure. Using phi-absolutely continuous functions, we obtain some approximations via summability process. Order of convergence is also observed. In addition, we have a general characterization theorem for phi-absolutely continuous functions. Finally, w...

In this study, we construct max-product and max-min kind pseudo-linear discrete operators. First, we obtain some approximation results for bounded and uniformly continuous functions. Then, the rate of convergence for these approximations using a suitable Lipschitz class of continuous functions is also discussed. Some applications for verifying our...

ATSF is an international conference series organized to bring together researchers from ALL areas of Approximation Theory and Special Functions to discuss new ideas and new applications. This organization, which has been held seven times so far as mini-symposia, has grown gradually over the years and will be held for the eighth time on September 4-...

In this note, we construct a pseudo-linear kind discrete operator based on the continuous and nondecreasing generator function. Then, we obtain an approximation to uniformly continuous functions through this new operator. Furthermore, we calculate the error estimation of this approach with a modulus of continuity based on a generator function. The...

In the literature, there are various methods to obtain the fractal sets such as escape time algorithm, L-systems and iterated function system (IFS), etc. In this study, we aim to approximate to the classical fractals by using non-affine contraction mappings. In order to get these non-affine map-pings, we utilize from the sequences of suitable Lipsc...

In this study, we construct Kantorovich variant of max-min kind operators, which are non-linear. By using these new operators, we obtain some uniform approximation results in N-dimension (N ≥ 1). Then, we estimate the error with the help of Hölder continuous functions and modulus of continuity. Furthermore, we give some illustrative applications to...

We consider convolution-type nonlinear integral operators endowed with Musielak-Orlicz φ -variation. Ouraim is to get more powerful approximation results with the help of summability methods. In this study, we use φ -absolutely continuous functions for our convergence results. Moreover, we study the order of approximation using suitableLipschitz cl...

In the present paper, our purpose is to obtain a nonlinear approximation by using convergence in ϕ-variation. Angeloni and Vinti prove some approximation results considering linear sampling-type discrete operators. These types of operators have close relationships with generalized sampling series. By improving Angeloni and Vinti's one, we aim to ge...

In this paper, we approximate to functions in N-dimension by means of nonlinear integral operators of the convolution type. Our approximation is based on not only the uniform norm but also the variation semi-norm in Tonelli's sense. We also study the rates of convergence. To get more general results we mainly use regular summability methods in the...

We investigate the approximation properties of nonlinear integral operators of the convolution type. In this approximation, we use functions of bounded variation based on the appropriate functionals. To get more general results, we consider Bell-type summability methods in the approximation. Moreover, we examine the rate of approximation. Then, usi...

In the present paper, by considering nonlinear integral operators and using their approximations via regular summability methods, we obtain characterizations for some function spaces including the space of absolutely continuous functions, the space of uniformly continuous functions, and their other variants. We observe that Bell-type summability me...

In this paper, we study the approximation properties of nonlinear integral operators of convolution-type by using summability process. In the approximation, we investigate the convergence with respect to both the variation semi-norm and the classical supremum norm. We also compute the rate of approximation on some appropriate function classes. At t...

In this study, approximation properties of the Mellin-type nonlin-ear integral operators defined on multivariate functions are investigated. In order to get more general results than the classical aspects, we mainly use the summability methods defined by Bell. Considering the Haar measure with variation semi-norm in Tonelli's sense, we approach to...

The summability process introduced by Bell (Proc Am Math Soc 38: 548–552, 1973) is a more general and also weaker method than ordinary convergence. Recent studies have demonstrated that using this convergence in classical approximation theory provides many advantages. In this paper, we study the summability process to approximate a function and its...