A result in best approximation theory

Sahab, Sareena; Khan, Muhammad Shoaib; Sessa, Salvatore

doi:10.1016/0021-9045(88)90101-3

Cited by 87 publications

(106 citation statements)

References 4 publications

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“…An application of new result is presented to best approximation theory; our work extends earlier results of Brosowski [3], Sahab et al [12], Singh [14] and many others.…”

Section: If I Is Affine and Nonexpansive In C And If T (C) ⊆ I(c) Thsupporting

confidence: 78%

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An extension of a theorem of Sahab, Khan, and Sessa

Khan

Hussain

2001

International Journal of Mathematics and Mathematical Sciences

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“…An application of new result is presented to best approximation theory; our work extends earlier results of Brosowski [3], Sahab et al [12], Singh [14] and many others.…”

Section: If I Is Affine and Nonexpansive In C And If T (C) ⊆ I(c) Thsupporting

confidence: 78%

“…(ii) Commuting maps satisfy (2.6) so Theorem 2.3(i) is a proper generalization of the main results of Sahab et al [12] and Singh [14].…”

Section: Ii) D a Is Weakly Compact In (E τ) I Is Weakly Continuous mentioning

confidence: 73%

An extension of a theorem of Sahab, Khan, and Sessa

Khan

Hussain

2001

International Journal of Mathematics and Mathematical Sciences

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“…In 1992, Beg et al [4] proved results on the existence of the best approximant for relatively contractive commuting mappings on convex metric spaces which also generalized the core result of Sahab et al [14]. In 1996, Al-Thagafi [1] established some theorems on invariant approximations for commuting maps.…”

Section: Introductionmentioning

confidence: 89%

“…In 1982, Hicks and Humpheries [6] generalized the results regarding invariant approximation. In the year 1988, Shahab et al [14] extended the results of Hicks and Humpheries [6] and Singh [17] by considering a pair of mappings wherein one is linear and the other one is nonexpansive.…”

Section: Introductionmentioning

confidence: 99%

A Result in Best Approximation Theory for Family of Maps

Rathee¹,

Reetu²

2014

IJCA

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“…Later, several results [7,25,27] have been proved in the direction of Brosowski [2]. In the year 1988, Sahab, Khan and Sessa [22] extended the result of Hicks and Humpheries [7] and Singh [25] by using two mappings, one linear and the other nonexpansive mappings for commuting mappings.…”

Section: Introductionmentioning

confidence: 97%

Common fixed point and best approximation for Banach operator pairs in non-starshaped domain

Nashine¹

2009

Demonstratio Mathematica

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Abstract. Common fixed point results for Banach operator pair with generalized nonexpansive mappings in non-starshaped domain of metric space have been obtained in the present work. As application, more general best approximation results in normed space have also been determined. These results extend and generalize various existing known results with the aid of Banach operator pair and without starshaped condition of domain. IntroductionFixed point theorems have been applied in the field of invariant approximation theory since last four decades and several interesting and valuable results have been studied. Meinardus [17] was the one to employ a fixed-point theorem of Schauder to establish the existence of an invariant approximation. Further, Brosowski [2] obtained a celebrated result and generalized the Meinardus's result. Later, several results [7,25,27]

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A result in best approximation theory

Cited by 87 publications

References 4 publications

An extension of a theorem of Sahab, Khan, and Sessa

An extension of a theorem of Sahab, Khan, and Sessa

A Result in Best Approximation Theory for Family of Maps

Common fixed point and best approximation for Banach operator pairs in non-starshaped domain

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