Document Details

Document Type : Project 
Document Title :
On Reich’s Problem
على نقطة بحثية لريتش
 
Subject : On Reich’s Problem 
Document Language : Arabic 
Abstract : The geometric fixed point theory for multi-valued maps was initiated by Nadler. Using the concept of Hausdorff metric, he has introduced a notion of multi-valued contraction maps and proved multi-valued version of the Banach Contraction Principle. In 1983 Reich has proposed the problem on the existence of fixed points for multi-valued maps that satisfy a certain contractive condition in the setting of metric spaces. Mizoguchi and Takahashi gave positive answer to the conjecture of Reich. Recently, Kada et al. have introduced a new concept of w-distance on a metric space and improved the Caristi’s fixed point theorem, Ekeland’s variational principle, and the nonconvex minimization theorem. Using the concept of w-distance, Suzuki and Takahashi proved some interesting fixed point results for multi-valued contractive maps without using the concept of Hausdorff metric. In this project, we want to study some alternative proofs concerning the positive response by Mizoguchi and Takahashi to the conjecture of Reich. Also, using the concept of w-distance, we want to obtain some general results on the existence of fixed points for multi-valued maps including the conjecture of Reich. 
Publishing Year : 1428 AH
2007 AD 
Sponsor Name : King Abdulaziz University 
Sponsorship Year : 1428 AH
2007 AD 
Added Date : Tuesday, July 13, 2010 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
عبداللطيف نور محمدMuhammad, Abdul Latif NoorInvestigatorDoctorate 

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