Generalized φ-contraction for four mappings on solid cone metric spaces

Abstract

In this paper we introduce the concept of a generalized φ-contraction for four mappings in solid cone metric spaces. Our results generalize, extend, unify, enrich and complement recent common fixed point results established by Chi-Ming Chen, Tong Huei Chang [Chi-Ming Chen, Tong-Huei Chang, Common fixed point theorems for a weaker Meir-Keeler type function in cone metric spaces, Applied Mathematics Letters 23 (2010) 1336-1341], I. Arand̂elović et al. [I. Arand̂elovié, Z. Kadelburg, S. Radenovicn;, Boyd-Wong-type common fixed point results in cone metric spaces, Applied Mathematics and Computation 217 (2011) 7167-7171] and A. Razani et al. [A. Razani, V. Rakočević, Z. Goodarzi, Generalized φcontraction for a pair of mappings on cone metric spaces, Applied Mathematics and Computation 217 (2011) 8899-8906]. Some examples are included which illustrate the cases when new results can be applied while old one cannot.