In this paper, we introduce $(p,q)$ -gamma operators which preserve $x^{2}$ , estimate the moments of these operators, and establish direct local approximation theorems operators. Then two about Lipschitz functions are obtained. The estimates on rate convergence some weighted also Furthermore, Voronovskaja-type asymptotic formula is presented.

Abstract In the present paper, we construct a new class of positive linear λ -Bernstein operators based on ( p , q )-integers. We obtain Korovkin type approximation theorem, study rate convergence these by using conception K -functional and moduli continuity, also give theorem for Lipschitz continuous functions.

Coenzyme Q (CoQ or ubiquinone) is a lipid-soluble component of virtually all types cell membranes and has been shown to play multiple metabolic functions. Several clinical diseases including encephalomyopathy, cerebellar ataxia isolated myopathy were be associated with CoQ deficiency. However, the role in immunity not defined. In present study, we showed that flies defective biosynthetic gene coq2 more susceptible bacterial fungal infections, while resistant viruses. We found Drosophila...

In this manuscript, we construct new modification of Baskakov operators on (0,?) using the second central moment classical operators. And moments and computation formulas their quantitative properties are computed. Then, rate convergence, point-wise estimates, weighted approximation Voronovskaya type theorem for established. Also, Kantorovich Durrmeyer generalizations discussed. Finally, some graphs numerical examples showed by Matlab algorithms.

We construct the Stancu-type generalization of q-Bernstein operators involving idea Bézier bases depending on shape parameter −1≤ζ≤1 and obtain auxiliary lemmas. discuss local approximation results in term a Lipschitz-type function based two parameters maximal function, as well other related for our newly constructed operators. Moreover, we determine rate convergence by means Peetre’s K-functional corresponding modulus continuity.

In this paper we propose the Stancu type generalization of a kind q-Gamma operators. We estimate moments these operators and establish two direct local approximation theorems also obtain estimates rate convergence weighted Furthermore, present Voronovskaya asymptotic formula. MSC:41A10, 41A25, 41A36.

In this paper, we propose the Stancu type generalization of a kind modified q-Gamma operators. We estimate moments these operators and give basic convergence theorem. also obtain Voronovskaja Furthermore, local approximation, rate weighted approximation for

We construct the blending-type modified Bernstein–Durrmeyer operators and investigate their approximation properties. First, we derive Voronovskaya-type asymptotic theorem for this type of operator. Then, local global theorems are obtained by using classical modulus continuity K-functional. Finally, rate convergence functions with a derivative bounded variation. The results show that new have good

In this paper, we introduce a family of bivariate α , q -Bernstein–Kantorovich operators and G B S (Generalized Boolean Sum) type. For the former, obtain estimate moments central moments, investigate degree approximation for these in terms partial moduli continuity Peetre’s K-functional. latter, rate convergence B-continuous B-differentiable functions by using mixed modulus smoothness.

In the present paper, we will introduce <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M3"><a:mi>λ</a:mi></a:math> -Gamma operators based on <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M4"><c:mi>q</c:mi></c:math> -integers. First, auxiliary results about moments are presented, and central of these also estimated. Then, discuss some local approximation properties by means modulus continuity Peetre <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M5"><e:mi...

In this paper, we introduce the q-analogue of modified Gamma operators preserving linear functions. We establish moments using q-Gamma Next, some local approximation for above are discussed. Also, rate convergence and weighted by these in terms modulus continuity studied. Furthermore, obtain Voronovskaja type theorem.

Abstract In this note, we study some approximation properties on a class of special Lototsky–Bernstein bases. We focus $|x|$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>|</mml:mo> <mml:mi>x</mml:mi> </mml:math> $[-1,1]$ <mml:mo>[</mml:mo> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mo>]</mml:mo> by an process generated from fixed points Our first result shows that the procedure $p_{n}(x)$ <mml:msub> <mml:mi>p</mml:mi> <mml:mi>n</mml:mi> </mml:msub>...

In this paper, a kind of new analogue Gamma type operators based on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mo stretchy="false">(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-integers is introduced. The Voronovskaja asymptotic formula these investigated. And some other results are studied by means modulus continuity and Peetre id="M3"><mml:mi>K</mml:mi><mml:mo>-</mml:mo></mml:math>functional....

This paper introduces noncommutative symmetric difference operators for fuzzy logics. Structures and properties of these are investigated. Finally, pseudo-quasi-metric pseudo-metric constructed on [0,1] based the differences.

In the present paper, generalized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi></mml:mrow></mml:mfenced></mml:math>-gamma-type operators based on id="M3"><mml:mfenced close=")"><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi></mml:mrow></mml:mfenced></mml:math>-calculus are introduced. The moments and central obtained, some local approximation properties of...

In this paper, we introduce a new analogue of Gamma operators and call it as (p,q) -Gamma which is generalization q operators.Moments these estimated.And some other results are studied by means modulus continuity Peetre K -functional.Then, theorems concerned with the rate convergence weighted approximation for also obtained.Finally, Voronovskaya asymptotic formula presented.

In this paper, we introduce a new kind of modified (<i>p, q</i>)-Szász-Mirakyan-Kantorovich operators based on q</i>)-calculus. Next, the moments computation formulas, second and fourth order central formulas other quantitative properties are investigated. Then, approximation including local approximation, weighted rate convergence Voronovskaja type theorem obtained. Finally, generalize by adding parameter <i>λ</i>.

In this paper, we construct stancu type generalization of (p, q)-Gamma operators: q)-Gamma-Stancu operators.We establish the auxiliary results on moments and central also discuss some local approximation properties these operators by means modulus continuity Peetre K-functional.Furthermore, investigate Voronovskaja theorem.

In this work, we extend the works of F. Usta and construct new modified <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M2"><a:mi>q</a:mi></a:math> -Bernstein operators using second central moment <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M3"><c:mi>q</c:mi></c:math> defined by G. M. Phillips. The moments computation formulas their quantitative properties are discussed. Also, Korovkin-type approximation theorem these Voronovskaja-type asymptotic formula investigated....

This paper generalizes a trigonometric inequality to sine integral and double series satisfying MVBVF( R + ) condition MVBVDS condition.

This paper presents a novel approach to addressing the challenges of manual on-site detection bridge cracks, including time-consuming, labor-intensive, low safety factor, and identification accuracy. The proposed method is based on an improved version YOLO v3 algorithm for crack object detection. achieves cracks. experimental results show that accuracy 90.26% test set has good recognition performance.

In this paper, we strengthen some of Leindler?s results from [L. Leindler. Embedding relations Besov classes. Acta Sci. Math. (Szeged), 73(2007) 133-149.] under MVBV condition. First, discuss embedding between two Next, give an equivalent estimate for the k-order modulus continuity f (x) in Lp norm Finally, condition to ensure a function ? having Fourier coefficients belongs class.

In the present article, we construct <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M2"> <a:mfenced open="(" close=")"> <a:mrow> <a:mi>p</a:mi> <a:mo>,</a:mo> <a:mi>q</a:mi> </a:mrow> </a:mfenced> </a:math> -Szász-Mirakjan-Kantorovich-Stancu operators with three parameters <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M3"> <e:mi>λ</e:mi> <e:mo>,</e:mo> <e:mi>α</e:mi> <e:mi>β</e:mi> </e:math> . First, moments and central are estimated. Then, local approximation properties...