Best proximity point results for generalized Θ-contractions and application to matrix equations

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Ma Z., Hussain A., Adeel M., Hussain N., SAVAŞ E.

Symmetry, vol.11, no.1, 2019 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.3390/sym11010093
  • Journal Name: Symmetry
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Best proximity point, α-ψ-contraction, Θ-contraction
  • Open Archive Collection: AVESIS Open Access Collection
  • Uşak University Affiliated: Yes

Abstract

In this paper, we introduce the notion of Ćirić type α-ψ-Θ-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 + ∑m i=1 Ai *υ(X)Ai and give a numerical example.