Global optimization using $\alpha$-ordered proximal contractions in metric spaces with partial orders

common best proximity point, global optimal approximate solution, proximally increasing mappings, $\alpha$-ordered contractions, $\alpha$-ordered proximal contraction, $\alpha$-ordered proximal cyclic contraction

Supporting agencies:

The Petchra Pra Jom Klao Doctoral Scholarship Academic

Abstract:

The purpose of this article is to establish the global optimization with partial orders for the pair of non-self mappings, by introducing new type of contractions like $\alpha$-ordered contractions and $\alpha$-ordered proximal contraction in the frame work of complete metric spaces. Also calculates some fixed point theorems with the help of these generalized contractions. In addition, established an example to show the validity of our main result. These results extended and unify many existing results in the literature.

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