Best Proximity Point and Existence of the Positive Definite Solution for Matrix Equations

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Satyendra Kumar Jain, Gopal Meena, Rashmi Jain

Abstract

In this research, α − ψ − θ contraction has been defined to find the best proximity point in partially ordered metric spaces. Proper support for the result has been given in the form of a suitable example. The third part is fully devoted to the positive definite solution of matrix equations.

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References

  1. A. Abkar, M. Gabeleh, Best Proximity Points for Cyclic Mappings in Ordered Metric Spaces, J. Optim. Theory Appl. 150 (2011), 188-193. https://doi.org/10.1007/s10957-011-9810-x.
  2. A. Abkar, M. Gabeleh, Generalized Cyclic Contractions in Partially Ordered Metric Spaces, Optim. Lett. 6 (2011), 1819-1830. https://doi.org/10.1007/s11590-011-0379-y.
  3. A. Abkar, M. Gabeleh, The Existence of Best Proximity Points for Multivalued Non-Self-Mappings, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM. 107 (2012), 319-325. https://doi.org/10.1007/s13398-012-0074-6.
  4. J. Ahmad, A.E. Al-Mazrooei, Y.J. Cho, et al. Fixed Point Results for Generalized Theta-Contractions, J. Nonlinear Sci. Appl. 10 (2017), 2350-2358. https://doi.org/10.22436/jnsa.010.05.07.
  5. S. Sadiq Basha, Extensions of Banach’s Contraction Principle, Numer. Funct. Anal. Optim. 31 (2010), 569–576. https://doi.org/10.1080/01630563.2010.485713.
  6. S.S. Basha, Discrete Optimization in Partially Ordered Sets, J. Glob. Optim. 54 (2011), 511-517. https://doi.org/10.1007/s10898-011-9774-2.
  7. M. Jleli, B. Samet, Best Proximity Point for α − ψ Contractive Type Mapping and Applications, Bull. Sci. Math. 137 (2013), 977-995.
  8. M. Jleli, B. Samet, A New Generalization of the Banach Contraction Principle, J Inequal Appl. 2014 (2014), 38. https://doi.org/10.1186/1029-242x-2014-38.
  9. V. Pragadeeswarar, M. Marudai, Best Proximity Points: Approximation and Optimization in Partially Ordered Metric Spaces, Optim. Lett. 7 (2012), 1883-1892. https://doi.org/10.1007/s11590-012-0529-x.
  10. V. Pragadeeswarar, M. Marudai, Best Proximity Points for Generalized Proximal Weak Contractions in Partially Ordered Metric Spaces, Optim. Lett. 9 (2013), 105-118. https://doi.org/10.1007/s11590-013-0709-3.
  11. H. Piri, S. Rahrovi, H. Marasi, et al. A Fixed Point Theorem for F-Khan-Contractions on Complete Metric Spaces and Application to Integral Equations, J. Nonlinear Sci. Appl. 10 (2017), 4564-4573. https://doi.org/10.22436/jnsa.010.09.02.
  12. A.C.M. Ran, M.C.B. Reurings, A Fixed Point Theorem in Partially Ordered Sets and Some Applications to Matrix Equations, Proc. Amer. Math. Soc. 132 (2003), 1435–1443.
  13. B. Samet, C. Vetro, P. Vetro, Fixed Point Theorem for α − ψ Contractive Mapping, Nonlinear Anal.: Theory Methods Appl. 75 (2012), 2154-2165. https://doi.org/10.1016/j.na.2011.10.014.
  14. J. Zhang, Y. Su, Q. Cheng, A note on ’A best proximity point theorem for Geraghty-contractions’, Fixed Point Theory Appl. 2013 (2013), 99. https://doi.org/10.1186/1687-1812-2013-99.