Application of Almost Convergence in Approximation Theorems for Functions of Two Variables

2014 ◽  
pp. 99-115
Author(s):  
M. Mursaleen ◽  
S. A. Mohiuddine
Keyword(s):  
Almost Convergence ◽  
Approximation Theorems ◽  
Functions Of Two Variables

On generalized Szász-Mirakyan operators of functions of two variables

2012 ◽  
Vol 62 (1) ◽  
Author(s):  
Lucyna Rempulska ◽  
Szymon Graczyk
Keyword(s):  
Exponential Weight ◽  
Approximation Theorems ◽  
Functions Of Two Variables

AbstractWe introduce certain generalized Szász-Mirakyan operators in exponential weight spaces of functions of two variables and we give approximation theorems for them.

scholarly journals Approximation Theorems for Functions of Two Variables viaσ-Convergence

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Mohammed A. Alghamdi
Keyword(s):  
Approximation Theorem ◽  
Bernstein Polynomials ◽  
Test Functions ◽  
Double Sequences ◽  
Korovkin Type Approximation Theorem ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Functions Of Two Variables

Çakan et al. (2006) introduced the concept ofσ-convergence for double sequences. In this work, we use this notion to prove the Korovkin-type approximation theorem for functions of two variables by using the test functions 1,x,y, andx2+y2and construct an example by considering the Bernstein polynomials of two variables in support of our main result.

scholarly journals A certain class of deferred weighted statistical B-summability involving (p,q)-integers and analogous approximation theorems

Filomat ◽  
2019 ◽  
Vol 33 (5) ◽  
pp. 1425-1444 ◽  
Author(s):  
Amjed Zraiqat ◽  
S.K. Paikray ◽  
Hemen Dutta
Keyword(s):  
Banach Space ◽  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Approximation Theorem ◽  
Difference Sequence ◽  
Bernstein Operators ◽  
Approximation Theorems ◽  
Functions Of Two Variables ◽  
The Difference

The preliminary idea of statistical weighted B-summability was introduced by Kadak et al. [27]. Subsequently, deferred weighted statistical B-summability has recently been studied by Pradhan et al. [38]. In this paper, we study statistical versions of deferred weighted B-summability as well as deferred weighted B-convergence with respect to the difference sequence of order r (> 0) involving (p,q)-integers and accordingly established an inclusion between them. Moreover, based upon our proposed methods, we prove an approximation theorem (Korovkin-type) for functions of two variables defined on a Banach space CB(D) and demonstrated that, our theorem effectively improves and generalizes most (if not all) of the existing results depending on the choice of (p,q)-integers. Finally, with the help of the modulus of continuity we estimate the rate of convergence for our proposed methods. Also, an illustrative example is provided here by generalized (p,q)-analogue of Bernstein operators of two variables to demonstrate that our theorem is stronger than its traditional and statistical versions.

scholarly journals Common Fixed Point and Invariant Approximation Results on Non-Starshaped Domains

2005 ◽  
Vol 12 (4) ◽  
pp. 659-669
Author(s):  
Nawab Hussain ◽  
Donal O'Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fréchet Spaces ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Invariant Approximation ◽  
Commuting Maps

Abstract We extend the concept of 𝑅-subweakly commuting maps due to Shahzad [J. Math. Anal. Appl. 257: 39–45, 2001] to the case of non-starshaped domains and obtain common fixed point results for this class of maps on non-starshaped domains in the setup of Fréchet spaces. As applications, we establish Brosowski–Meinardus type approximation theorems. Our results unify and extend the results of Al-Thagafi, Dotson, Habiniak, Jungck and Sessa, Sahab, Khan and Sessa and Shahzad.

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