THE ORDER-CONVERGENCE OF THE THAKUR ITERATIVE PROCESS FOR HARDY-ROGERS CONTRACTIONS IN ORDER-BANACH SPACES.

This paper proves several fixed point results for mappings satisfying the Hardy-Rogers inequality on order-metric spaces. Using ordered vector space valued norm-type mappings, the concept of completeness is redefined resulting order-Banach spaces. One of the main outcomes proves that each Dedekind σ-complete Riesz space is complete with respect to its natural absolute value. This statement leads to consistent examples of order-Banach structures. Ultimately, the Thakur iterative process is analyzed in the newly defined order-Banach framework; it results that the Thakur iteration orderconverges faster than the Picard iterative process, for the class of Hardy-Rogers contractions. [ABSTRACT FROM AUTHOR]