IJPAM: Volume 107, No. 1 (2016)


Godwin Amechi Okeke$^1$, Kanayo Stella Eke$^2$
$^1$Department of Mathematics
Michael Okpara University of Agriculture
Umudike, P.M.B. 7267, Umuahia, Abia State, NIGERIA
$^2$Department of Mathematics
College of Science and Technology
Covenant University
Canaanland, KM 10 Idiroko Road, P.M.B. 1023 Ota
Ogun State, NIGERIA

Abstract. The purpose of this study is to introduce a Noor-type random iterative scheme and prove the convergence of this kind of random iterative scheme for certain $\phi$-weakly contractive type random operators. The Bochner integrability of random fixed points for this kind of random operators and the almost sure $T$-stability and convergence for Noor-type random iterative scheme are established. Our results are stochastic generalizations of the deterministic fixed point theorems of Berinde [#!BERINDE2002!#,#!BERINDE2004!#] and Rhoades [#!RHOADES1974!#]-[#!RHOADES2001!#].

Received: June 12, 2015

AMS Subject Classification: 47H09, 47H10, 49M05, 54H25

Key Words and Phrases: Bochner integrability, Noor-type random iterative scheme, almost sure $T$-stability, random fixed point

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DOI: 10.12732/ijpam.v107i1.1 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 107
Issue: 1
Pages: 1 - 16

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