Fixed Point Theory and Applications 
Volume 2008 (2008), Article ID 916187, 6 pages
doi:10.1155/2008/916187
Research Article

Quasicontraction Mappings in Modular Spaces without Δ2-Condition

M. A. Khamsi

 Department of Mathematical Science, The University of Texas at El Paso, El Paso, TX 79968, USA
Received 22 May 2008; Accepted 1 July 2008

Recommended by William A. Kirk

Abstract

As a generalization to Banach contraction principle, Ćirić introduced the concept of quasi-contraction mappings. In this paper, we investigate these kinds of mappings in modular function spaces without the Δ2-condition. In particular, we prove the existence of fixed points and discuss their uniqueness.