# IJPAM: Volume 109, No. 4 (2016)

**RANDOM COMMON FIXED POINT THEOREM FOR**

RANDOM WEAKLY SUBSEQUENTIALLY CONTINUOUS

GENERALIZED CONTRACTIONS WITH APPLICATION

RANDOM WEAKLY SUBSEQUENTIALLY CONTINUOUS

GENERALIZED CONTRACTIONS WITH APPLICATION

Rashwan A. Rashwan, Hasanen A. Hammad

Department of Mathematics

Faculty of Science

Assuit University

Assuit, 71516, EGYPT

Department of Mathematics

Faculty of Science

Sohag University

Sohag, 82524, EGYPT

Department of Mathematics

Faculty of Science

Assuit University

Assuit, 71516, EGYPT

Department of Mathematics

Faculty of Science

Sohag University

Sohag, 82524, EGYPT

**Abstract.**In this paper, we prove random common fixed point theorem for two pairs of random self mappings under a generalized contractive condition using subsequential continuity with compatibility of type (E). An example is given to justify our theorem. Our results in randomness extend and improve the results of S. Beloul [4]. Finally, we give an application to discuss the existence of a solution of random Hammerstein integral equations.

**Received:**July 14, 2016

**Revised:**August 18, 2016

**Published: **October 9, 2016

**AMS Subject Classification: **47H10, 24H25

**Key Words and Phrases: **polish spaces, random operators, compatible of type (E), weakly subsequentially continuous
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# .

**DOI: 10.12732/ijpam.v109i4.5**

International Journal of Pure and Applied Mathematics

**How to cite this paper?****Source:****ISSN printed version:**1311-8080

**ISSN on-line version:**1314-3395

**Year:**2016

**Volume:**109

**Issue:**4

**Pages:**813 - 826

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**This work is licensed under the Creative Commons Attribution International License (CC BY).**