Approximation theorems for Pascali systems

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

Georgian Mathematical Journal ◽

10.1515/gmj.2005.659 ◽

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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DENSE STABLE RANK AND RUNGE-TYPE APPROXIMATION THEOREMS FOR MAPS

Journal of the Australian Mathematical Society ◽

10.1017/s1446788721000045 ◽

2021 ◽

pp. 1-29

Author(s):

ALEXANDER BRUDNYI

Keyword(s):

Disjoint Union ◽

A Priori ◽

Holomorphic Functions ◽

Stable Rank ◽

Open Unit ◽

Uniform Estimates ◽

Approximation Theorems ◽

Type Approximation ◽

Similar Approximation ◽

Bounded Holomorphic

Abstract Let $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ be the Banach algebra of bounded holomorphic functions defined on the disjoint union of countably many copies of the open unit disk ${\mathbb {D}}\subset {{\mathbb C}}$ . We show that the dense stable rank of $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ is $1$ and, using this fact, prove some nonlinear Runge-type approximation theorems for $H^\infty ({\mathbb {D}}\times {\mathbb {N}})$ maps. Then we apply these results to obtain a priori uniform estimates of norms of approximating maps in similar approximation problems for the algebra $H^\infty ({\mathbb {D}})$ .

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Approximation Theorems for Localized Baskakov Operators

Numerical Functional Analysis and Optimization ◽

10.1080/01630563.2021.1881971 ◽

2021 ◽

pp. 1-14

Author(s):

Linsen Xie ◽

Tingfan Xie ◽

Hong Du

Keyword(s):

Baskakov Operators ◽

Approximation Theorems

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Approximation theorems of a solution of amperometric enzymatic reactions based on Green’s fixed point normal-S iteration

Advances in Difference Equations ◽

10.1186/s13662-021-03289-w ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Khanitin Muangchoo-in ◽

Kanokwan Sitthithakerngkiet ◽

Parinya Sa-Ngiamsunthorn ◽

Poom Kumam

Keyword(s):

Fixed Point ◽

Boundary Value Problems ◽

Iterative Methods ◽

Dynamical Problem ◽

Enzymatic Reactions ◽

Nonlinear Dynamical ◽

Numerical Examples ◽

Approximation Theorems ◽

Kinetics Of ◽

Nonlinear Dynamical Problem

AbstractIn this paper, the authors present a strategy based on fixed point iterative methods to solve a nonlinear dynamical problem in a form of Green’s function with boundary value problems. First, the authors construct the sequence named Green’s normal-S iteration to show that the sequence converges strongly to a fixed point, this sequence was constructed based on the kinetics of the amperometric enzyme problem. Finally, the authors show numerical examples to analyze the solution of that problem.

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Direct and inverse approximation theorems of functions in the Orlicz type spaces 𝓢M

Mathematica Slovaca ◽

10.1515/ms-2017-0314 ◽

2019 ◽

Vol 69 (6) ◽

pp. 1367-1380 ◽

Cited By ~ 2

Author(s):

Stanislav Chaichenko ◽

Andrii Shidlich ◽

Fahreddin Abdullayev

Keyword(s):

Fractional Order ◽

Moduli Of Smoothness ◽

Best Approximations ◽

Approximation Theorems ◽

Inverse Approximation ◽

Type Spaces

Abstract In the Orlicz type spaces 𝓢M, we prove direct and inverse approximation theorems in terms of the best approximations of functions and moduli of smoothness of fractional order. We also show the equivalence between moduli of smoothness and Peetre K-functionals in the spaces 𝓢M.

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