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Ma, Zhenhua; Hussain, Azhar; Adeel, Muhammad; Hussain, Nawab; Savas, Ekrem

Best proximity point results for generalized \(\Theta\)-contractions and application to matrix equations. (English) Zbl 1423.47029

Symmetry 11, No. 1, Paper No. 93, 20 p. (2019).
Summary: In this paper, we introduce the notion of Ćirić type \(\alpha\)-\(\psi\)-\(\Theta\)-contraction and prove best proximity point results in the context of complete metric spaces. Moreover, we prove some best proximity point results in partially ordered complete metric spaces through our main results. As a consequence, we obtain some fixed point results for such contraction in complete metric and partially ordered complete metric spaces. Examples are given to illustrate the results obtained. Moreover, we present the existence of a positive definite solution of nonlinear matrix equation \(X=Q+\sum\limits_{i=1}^m A_i^\ast \gamma(X) A_i\) and give a numerical example.

Cited in 4 Documents

MSC:

47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
15A24 Matrix equations and identities

Keywords:

\(\Theta\)-contraction; \(\alpha\)-\(\psi\)-contraction; best proximity point
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