IJPAM: Volume 120, No. 4 (2018)

Title

FIXED-POINT AND BEST APPROXIMATION
THEOREMS IN MODULAR SPACES

Authors

Salwa Salman Abed$^1$, Karrar Emad Abdul Sada$^2$
$^{1,2}$Department of Mathematics
College of Education for Pure Sciences
Ibn Al-Haitham, Baghdad University

Abstract

In this paper, we prove that two fixed point theorems for compact set-valued mappings in modular spaces. As application, a result on invariant best approximation is proved.

History

Received: October 4, 2017
Revised: January 22, 2019
Published: January 28, 2019

AMS Classification, Key Words

AMS Subject Classification: 47H10, 46A80
Key Words and Phrases: modular spaces, fixed points, best approximations

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Bibliography

1
H. Nakano, Modular semi-ordered spaces, Tokyo Mathematical Book Series, Maruzen Co. Ltd, Tokyo, Japan, (1950).

2
J. Musielak and W. Ortiz, on modular spaces, Studia Math, 18, 49–65.A(1959).

3
M. Abbas, S.H. Khan and A. Razani, Fixed point theorems of expansive type mappings in modular function spaces, Fixed Point Theory, 12, No 2. 235–240(2011).

4
Kuaket, K. Kumam, P Fixed points of asymptotic point wise contractions in modular spaces. Appl. Math. Let. 24,1795-1798 (2011).

5
W.M. Kozlowski, Advancements in fixed point theory in modular function spaces, Arab J. Math,1, 477–494(2012). Doi: 10.1007/s40065-012-0051-0.

6
R. Chen, X. Wang, Fixed point of nonlinear contractions in modular spaces, J. of Ineq. And Appl. 2013, (2013).

7
S.S. Abed, on invariant best approximation in modular spaces, Glob. J. Pur. and Appl. Math., Vol 13, No 9, 5227-5233(2017).

8
S.S. Abed, K.A. Abdul Sada,, An Extension of Brosowski- Meinaraus Theorem in Modular Spaces, accepted in International Journal of Mathematical Analysis, Hikari Ltd.

9
S. Kakutani, A generalization of Brower's fixed point theorem, Duke Math .J.8 457-459(1941).

How to Cite?

DOI: 10.12732/ijpam.v120i4.4 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 120
Issue: 4
Pages: 541 - 546


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