Abdul Wafi - Academia.edu (original) (raw)

Papers by Abdul Wafi

In this article, we construct Bivariate-Bernstein -Chlodowsky operators based on (p, q)-integers.... more In this article, we construct Bivariate-Bernstein -Chlodowsky operators based on (p, q)-integers. We give the basic estimates for these operators. Moreover, we discuss rate of convergence and pointwise approximation in Lipschitz class. In the last, we prove weighted approximation results.

Cogent Mathematics, 2016

A generalization of Szász-type operators which preserves constant and quadratic test functions Re... more A generalization of Szász-type operators which preserves constant and quadratic test functions Recently, Varma and Taşdelen [85] defined Szász type operators via Charlier polynomials [46] with generating function of the form:

Journal of Mathematics and Applications, 2017

In present article, we discuss voronowskaya type theorem, weighted approximation in terms of weig... more In present article, we discuss voronowskaya type theorem, weighted approximation in terms of weighted modulus of continuity for Szász type operators using Sheffer polynomials. Lastly, we investigate statistical approximation for these sequences.

The aim of this article is to introduces a Stancu type generalization of modified Sz ´ asz operat... more The aim of this article is to introduces a Stancu type generalization of modified Sz ´ asz operators using Charlierpolynomials. We established a recursive relation between Sz ´ asz-type operators defined in [9] and Stancu-typegeneralization of these operators. Further, we discussed Korovkin type theorem, rate of convergence in terms ofmodulus of continuity and simultaneous approximation. Moreover, we studied Local approximation results usingsecond order modulus of smoothness, Peetre’s K-functional and Lipschitz class. In the last of this manuscript, wegave weighted Korovkin type theorem and statistical approximation result in polynomial weighted space.

Filomat, 2015

In the present paper, we introduce alpha;beta-variant of generalized Baskakov operators and study... more In the present paper, we introduce alpha;beta-variant of generalized Baskakov operators and study the rate of convergence using modulus of continuity, order of approximation for the derivative of function f . Direct estimate is proved using K-functional and Ditzian-Totik modulus of smoothness. In the last, we have proved Voronovskaya type theorem.

The aim of this article is to introduce a new form of Kantorovich Sz\'{a}sz-type operators in... more The aim of this article is to introduce a new form of Kantorovich Sz\'{a}sz-type operators involving Charlier polynomials. In this manuscript, we discuss the rate of convergence, better error estimates. Further, we investigate order of approximation in the sense of local approximation results with the help of Ditzian-Totik modulus of smoothness, second order modulus of continuity, Peetre's K-functional and Lipschitz class.

In the present article, we introduce a generalization of Szász-type operators which preserves tes... more In the present article, we introduce a generalization of Szász-type operators which preserves test functions e0 and e2 (ei = t i, i = 0, 2). By these sequence of positive linear operators, we give better error estimation analytically using modulus of continuity. Moreover, we have shown the better approximation graphically. Further, weighted Korovkin and Voronovskaya type theorems are established. MSC: 41A25; 41A36

Filomat

In this article, we construct Bivariate-Bernstein-Chlodowsky operators based on (p,q)-integers. W... more In this article, we construct Bivariate-Bernstein-Chlodowsky operators based on (p,q)-integers. We give the basic estimates for these operators. Moreover, we discuss rate of convergence and pointwise approximation in Lipschitz class. In the last, we prove weighted approximation results.

Iranian Journal of Science and Technology, Transactions A: Science

In this article, we introduce Szász–Gamma operators based on Dunkl analogue. We discuss basic app... more In this article, we introduce Szász–Gamma operators based on Dunkl analogue. We discuss basic approximation results in terms of the classical Korovkin theorem and modulus of continuity. For our operators, we investigate local approximation results by means of Peetre’s K-functional, second order modulus of smoothness, the Lipschitz class and the Lipschitz maximal function. Next, we present weighted approximation theorems by means of a Korovkin type theorem and weighted modulus of continuity. Lastly, A-Statistical approximation result and rate of convergence for functions with derivative of bounded variation are also studied.

Filomat

The aim of this article is to introduce a bivariate extension of Schurer-Stancu operators based o... more The aim of this article is to introduce a bivariate extension of Schurer-Stancu operators based on (p,q)-integers. We prove uniform approximation by means of Bohman-Korovkin type theorem, rate of convergence using total modulus of smoothness and degree of approximation via second order modulus of smoothness, Peetre?s K-functional, Lipschitz type class.

Demonstratio Mathematica

In this paper, we introduce the q-analogue of the Jakimovski-Leviatan type modified operators int... more In this paper, we introduce the q-analogue of the Jakimovski-Leviatan type modified operators introduced by Atakut with the help of the q-Appell polynomials.We obtain some approximation results via the well-known Korovkin’s theorem for these operators.We also study convergence properties by using the modulus of continuity and the rate of convergence of the operators for functions belonging to the Lipschitz class. Moreover,we study the rate of convergence in terms of modulus of continuity of these operators in aweighted space.

Complex Analysis and Operator Theory, 2017

their knowledge and understanding of their generation Y employees. Adapting management and leader... more their knowledge and understanding of their generation Y employees. Adapting management and leadership strategies according to these findings could lead to higher staff satisfaction, resulting in workforce productivity and increased profitability.

Applied Mathematics & Information Sciences Letters, 2016

Indian Journal of Pure and Applied Mathematics

ON THE APPROXIMATION OF FUNCTIONS BY GENERAL ORTHONORMAL POLYNOMIALS ON A FINITE SEGMENT

In this article, we have introduced (p;q)-variant of Stancu-Schurer operators and discussed the r... more In this article, we have introduced (p;q)-variant of Stancu-Schurer operators and discussed the rate of convergence for continuous functions. We have also discussed recursive estimates Korovkin and direct approximation results using second order modulus of continuity, Peetres K-functional Lipschitz class.

Disertasi Dan Tesis Program Pascasarjana Um, Jul 15, 2011

Indian Journal of Pure and Applied Mathematics, 1980

In the present paper, we introduce Stancu-variant of generalized Baskakov operators and study the... more In the present paper, we introduce Stancu-variant of generalized Baskakov operators and study the rate of convergence using modulus of continuity, order of approximation for the derivative of function f . Direct estimate is proved using K-functional and Ditzian-Totik modulus of smoothness. In the last, we have proved Voronovskaya type theorem.

In this article, we construct Bivariate-Bernstein -Chlodowsky operators based on (p, q)-integers.... more In this article, we construct Bivariate-Bernstein -Chlodowsky operators based on (p, q)-integers. We give the basic estimates for these operators. Moreover, we discuss rate of convergence and pointwise approximation in Lipschitz class. In the last, we prove weighted approximation results.

Cogent Mathematics, 2016

A generalization of Szász-type operators which preserves constant and quadratic test functions Re... more A generalization of Szász-type operators which preserves constant and quadratic test functions Recently, Varma and Taşdelen [85] defined Szász type operators via Charlier polynomials [46] with generating function of the form:

Journal of Mathematics and Applications, 2017

In present article, we discuss voronowskaya type theorem, weighted approximation in terms of weig... more In present article, we discuss voronowskaya type theorem, weighted approximation in terms of weighted modulus of continuity for Szász type operators using Sheffer polynomials. Lastly, we investigate statistical approximation for these sequences.

The aim of this article is to introduces a Stancu type generalization of modified Sz ´ asz operat... more The aim of this article is to introduces a Stancu type generalization of modified Sz ´ asz operators using Charlierpolynomials. We established a recursive relation between Sz ´ asz-type operators defined in [9] and Stancu-typegeneralization of these operators. Further, we discussed Korovkin type theorem, rate of convergence in terms ofmodulus of continuity and simultaneous approximation. Moreover, we studied Local approximation results usingsecond order modulus of smoothness, Peetre’s K-functional and Lipschitz class. In the last of this manuscript, wegave weighted Korovkin type theorem and statistical approximation result in polynomial weighted space.

Filomat, 2015

In the present paper, we introduce alpha;beta-variant of generalized Baskakov operators and study... more In the present paper, we introduce alpha;beta-variant of generalized Baskakov operators and study the rate of convergence using modulus of continuity, order of approximation for the derivative of function f . Direct estimate is proved using K-functional and Ditzian-Totik modulus of smoothness. In the last, we have proved Voronovskaya type theorem.

The aim of this article is to introduce a new form of Kantorovich Sz\'{a}sz-type operators in... more The aim of this article is to introduce a new form of Kantorovich Sz\'{a}sz-type operators involving Charlier polynomials. In this manuscript, we discuss the rate of convergence, better error estimates. Further, we investigate order of approximation in the sense of local approximation results with the help of Ditzian-Totik modulus of smoothness, second order modulus of continuity, Peetre's K-functional and Lipschitz class.

In the present article, we introduce a generalization of Szász-type operators which preserves tes... more In the present article, we introduce a generalization of Szász-type operators which preserves test functions e0 and e2 (ei = t i, i = 0, 2). By these sequence of positive linear operators, we give better error estimation analytically using modulus of continuity. Moreover, we have shown the better approximation graphically. Further, weighted Korovkin and Voronovskaya type theorems are established. MSC: 41A25; 41A36

Filomat

In this article, we construct Bivariate-Bernstein-Chlodowsky operators based on (p,q)-integers. W... more In this article, we construct Bivariate-Bernstein-Chlodowsky operators based on (p,q)-integers. We give the basic estimates for these operators. Moreover, we discuss rate of convergence and pointwise approximation in Lipschitz class. In the last, we prove weighted approximation results.

Iranian Journal of Science and Technology, Transactions A: Science

In this article, we introduce Szász–Gamma operators based on Dunkl analogue. We discuss basic app... more In this article, we introduce Szász–Gamma operators based on Dunkl analogue. We discuss basic approximation results in terms of the classical Korovkin theorem and modulus of continuity. For our operators, we investigate local approximation results by means of Peetre’s K-functional, second order modulus of smoothness, the Lipschitz class and the Lipschitz maximal function. Next, we present weighted approximation theorems by means of a Korovkin type theorem and weighted modulus of continuity. Lastly, A-Statistical approximation result and rate of convergence for functions with derivative of bounded variation are also studied.

Filomat

The aim of this article is to introduce a bivariate extension of Schurer-Stancu operators based o... more The aim of this article is to introduce a bivariate extension of Schurer-Stancu operators based on (p,q)-integers. We prove uniform approximation by means of Bohman-Korovkin type theorem, rate of convergence using total modulus of smoothness and degree of approximation via second order modulus of smoothness, Peetre?s K-functional, Lipschitz type class.

Demonstratio Mathematica

In this paper, we introduce the q-analogue of the Jakimovski-Leviatan type modified operators int... more In this paper, we introduce the q-analogue of the Jakimovski-Leviatan type modified operators introduced by Atakut with the help of the q-Appell polynomials.We obtain some approximation results via the well-known Korovkin’s theorem for these operators.We also study convergence properties by using the modulus of continuity and the rate of convergence of the operators for functions belonging to the Lipschitz class. Moreover,we study the rate of convergence in terms of modulus of continuity of these operators in aweighted space.

Complex Analysis and Operator Theory, 2017

their knowledge and understanding of their generation Y employees. Adapting management and leader... more their knowledge and understanding of their generation Y employees. Adapting management and leadership strategies according to these findings could lead to higher staff satisfaction, resulting in workforce productivity and increased profitability.

Applied Mathematics & Information Sciences Letters, 2016

Indian Journal of Pure and Applied Mathematics

ON THE APPROXIMATION OF FUNCTIONS BY GENERAL ORTHONORMAL POLYNOMIALS ON A FINITE SEGMENT

In this article, we have introduced (p;q)-variant of Stancu-Schurer operators and discussed the r... more In this article, we have introduced (p;q)-variant of Stancu-Schurer operators and discussed the rate of convergence for continuous functions. We have also discussed recursive estimates Korovkin and direct approximation results using second order modulus of continuity, Peetres K-functional Lipschitz class.

Disertasi Dan Tesis Program Pascasarjana Um, Jul 15, 2011

Indian Journal of Pure and Applied Mathematics, 1980

In the present paper, we introduce Stancu-variant of generalized Baskakov operators and study the... more In the present paper, we introduce Stancu-variant of generalized Baskakov operators and study the rate of convergence using modulus of continuity, order of approximation for the derivative of function f . Direct estimate is proved using K-functional and Ditzian-Totik modulus of smoothness. In the last, we have proved Voronovskaya type theorem.