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Öğe A-Statistical Korovkin-Type Approximation Theorem For Functions Of Two Variables On An Infinite Interval(Acta Mathematica Universitatis Comenianae, 2012) Demirci, Kamil; Karakuş, SevdaIn this paper, using the concept of A-statistical convergence for double sequences, we provide a Korovkin-type approximation theorem for positive linear operators on the space of all real-valued uniform continuous functions on [0;?) x [0;?) with the property that have a finite limit at the infinity. Then, we display an application which shows that our new result is stronger than its classical version.Öğe Approximation for periodic functions via statistical A-summability(Acta Mathematica Universitatis Comenianae, 2012) Demirci, Kamil; Karakuş, Sevda;In this paper, using the concept of statistical A-summability which is stronger than the A-statistical convergence, we prove a Korovkin type approxima-tion theorem for sequences of positive linear operator de ned on C (R) which is the space of all 2 -periodic and continuous functions on R, the set of all real numbers. We also compute the rates of statistical A-summability of sequence of positive linear operators.Öğe Approximation in statistical sense by n?multiple sequences of fuzzy positive linear operators(Studia Universitatis Babeş-Bolyai -- Series Mathematica, 2012) Demirci, Kamil; Karakuş, SevdaOur primary interest in the present paper is to prove a Korovkin- type approximation theorem for n ? multiple sequences of fuzzy positive linear operators via statistical convergence. Also, we display an example such that our method of convergence is stronger than the usual convergence.Öğe Equi-Statistical Extension of the Korovkin Type Approximation Theorem(Turkish Journal of Mathematics, 2009) Karakuş, Sevda; Demirci, KamilIn this paper using equi-statistical convergence, which is stronger than the usual uniform convergence and statistical uniform convergence, we obtain a general Korovkin type theorem. Then, we construct examples such that our new approximation result works but its classical and statistical cases do not work.Öğe Erratum to "Equi-statistical extension of the korovkin type approximation theorem" [Turk. J. Math. 33 (2009), 159-168](2009) Karakuş, Sevda; Demirci, Kamil[No abstract available]Öğe Four-dimensional matrix transformation and A-statistical fuzzy Korovkin type approximation(Demonstratio Mathematica, 2013) Demirci, Kamil; Karakuş, SevdaIn this paper, we prove a fuzzy Korovkin-type approximation theorem for fuzzy positive linear operators by using A-statistical convergence for four-dimensional summability matrices. Also, we obtain rates of A-statistical convergence of a double sequence of fuzzy positive linear operators for four-dimensional summability matrices.Öğe I and I* convergent function sequences(Mathematical Communications, 2005) Gezer, F.; Karakuş, SevdaIn this paper, we introduce the concepts of I-pointwise convergence, I-uniform convergence,I*-pointwise convergence and I*-uniform convergence of function sequences and then we examine the relation between them.Öğe Matrix Summability and Korovkin Type Approximation Theorem on Modular Spaces(Acta Mathematica Universitatis Comenianae, 2010) Karakuş, Sevda; Demirci, Kamil; info:eu-repo/semantics/openAccessIn this paper, using a matrix summability method we obtain a Korovkin type approximation theorem for a sequence of positive linear operators defined on a modular space.Öğe Statistical Convergence of Double Sequences on Probabilistic Normed Spaces(International Journal of Mathematics and Mathematical Sciences, 2007) Karakuş, Sevda; Demirci, KamilThe concept of statistical convergence was presented by Steinhaus in 1951. This concept was extended to the double sequences by Mursaleen and Edely in 2003. Karakus has recently introduced the concept of statistical convergence of ordinary (single) sequence on probabilistic normed spaces. In this paper, we define statistical analogues of convergence and Cauchy for double sequences on probabilistic normed spaces. Then we display an exampl e such that our method of convergence is stronger than usual convergence on probabilistic normed spaces. Also we give a useful characterization for statistically convergent double sequences.Öğe Statistical convergence on probalistic normed spaces(Mathematical Communications, 2007) Karakuş, SevdaIn this paper we define concepts of statistical convergence and statistical Cauchy on probabilistic normed spaces. Then we give a useful characterization for statistically convergent sequences. Furthermore, we display an example such that our method of convergence is stronger than the usual convergence on probabilistic normed spaces. We also introduce statistical limit points, statistical cluster points on probabilistic normed spaces and then we give the relations between these and limit points of sequence on probabilistic normed spaces.Öğe Statistical Limit Points of Sequences on Intuitionistic Fuzzy Normed Spaces(Journal of Concrete and Applicable Mathematics, 2008) Karakuş, Sevda; Demirci, Kamil; Yardımcı, ŞeyhmusKaraku?s, Demirci, Duman [Chaos, Solitons and Fractals (2006), doi: 10.1016/j.chaos.2006.05.046.] has recently introduced the notion of statis- tical convergence on intuitionistic fuzzy normed spaces. Using this notion, we study the concept of statistical limit points, statistical cluster points on intuitionistic fuzzy normed spaces and then we give the relations be- tween these and limit points of sequence on intuitionistic fuzzy normed spaces and also we give some topological properties.Öğe Summation Process Of Korovkin Type Approximation Theorem(Miskolc Mathematical Notes, 2011) Karakuş, Sevda; Demirci, Kamil[Abstract Not Available]
