Fixed point theory for generalized quasicontraction maps in vector modular spaces

Abstract

In this paper, we introduce vector modular spaces and prove the existence of fixed points for generalized quasicontraction maps and discuss their uniqueness in these spaces. Our fixed point theorem, even in the case of modular spaces, extends the main result of Khamsi [M.A. Khamsi, Quasicontraction mappings in modular spaces without Δ2-condition, Fixed Point Theory and Applications 2008, 6 pages, ID 916187]. © 2011 Elsevier Ltd. All rights reserved.