Erratum to ‘Coupled fixed point theorems for α-ψ-contractive type mappings in partially ordered metric spaces’

Abstract

In this note we present some corrections on our previous paper (Fixed Point Theory Appl. 2012:228, 2012).

In the paper [1], the following corrections are required on pages 3 and 6.

Inequality (3.1) in Theorem 3.4 on page 3 and the same inequality in Theorem 3.5 on page 6 should read as follows:

$$\alpha ((x,y),(u,v))\frac{d(F(x,y),F(u,v))+d(F(y,x),F(v,u))}{2}\le \psi \left(\frac{d(x,u)+d(y,v)}{2}\right).$$

The corresponding changes in the proofs of these theorems will lead to the conclusions easily. Moreover, we can easily choose suitable $F(x,y)$ in Examples 3.7 and 3.8 to meet our requirements.