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

Somayya Komal, Poom Kumam


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.


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

Subject classification

58C30; 47H10.

Full Text:



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