IJPAM: Volume 109, No. 2 (2016)

ON NEW ITERATION FOR SET CONTRACTION MAPPINGS
AND EXISTENCE RESULTS FOR POWER SET
CONTRACTIONS MAPPINGS

Nour El Houda Bouzara$^1$, Vatan Karakaya$^2$
$^{1,2}$Department of Mathematics
Yildiz Technical University
Davutpasa Campus
Esenler, Istanbul, 34220, TURKEY


Abstract. In this paper, we present a new iteration for set contraction mappings in a Banach space. In further, we introduce the concept of set stability for these class of mappings. Finally, we present some results on the existence of fixed points for power set contraction mappings, these results include in special case many results existing in literature like Darbo and generalized Darbo fixed point theorems.

Received: March 8, 2016

AMS Subject Classification: 47H10, 47H08

Key Words and Phrases: set contraction, measure of noncompactness, fixed point, iteration, stability

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DOI: 10.12732/ijpam.v109i2.3 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: 2016
Volume: 109
Issue: 2
Pages: 193 -


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