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New fixed point theorems for \({\alpha}\)-\({H\Theta}\)-contractions in ordered metric spaces

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Abstract

Recently, Jleli and Samet [J. Inequal. Appl. (2014), 2014:38] introduced and studied a new contraction to prove a generalization of the Banach contraction principle. In this paper, we introduce the concept of \({\alpha}\)-\({H\Theta}\)-contraction with respect to a general family of functions H and we establish Jleli–Samet-type fixed point results in metric and ordered metric spaces. As an application of our results we deduce Suzuki-type fixed point results for \({H\Theta}\)-contractions. We also derive certain fixed and periodic point results for orbitally continuous generalized \({\Theta}\)-contractions. Moreover, we present an illustrative example to highlight the obtained improvements.

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References

  1. M. Abbas, B. Ali and S. Romaguera, Fixed and periodic points of generalized contractions in metric spaces. Fixed Point Theory Appl. 2013 (2013), doi:10.1186/1687-1812-2013-243.

  2. R. P. Agarwal, N. Hussain and M. A. Taoudi, Fixed point theorems in ordered Banach spaces and applications to nonlinear integral equations. Abstr. Appl. Anal. 2012 (2012), Article ID 245872, 15 pages.

  3. Sh. Fathollahi, N. Hussain and L. A. Khan, Fixed point results for modified weak and rational \({\alpha}\)-\({\psi}\) -contractions in ordered 2-metric spaces. Fixed Point Theory Appl. 2014 (2014), doi:10.1186/1687-1812-2014-6.

  4. M. Jleli and B. Samet, A new generalization of the Banach contraction principle. J. Inequal. Appl. 2014 (2014), doi:10.1186/1029-242X-2014-38.

  5. Hussain N., Ahmad J., Azam A.: On Suzuki-Wardowski type fixed point theorems. J. Nonlinear Sci. Appl. 8, 1095–1111 (2015)

    MathSciNet  MATH  Google Scholar 

  6. Hussain N., Arshad M., Abbasa M., Hussain A.: Generalized dynamic process for generalized (f, L)-almost F-contraction with applications. J. Nonlinear Sci. Appl. 9, 1702–1715 (2016)

    MathSciNet  MATH  Google Scholar 

  7. N. Hussain, D. Dorić, Z. Kadelburg and S. Radenović, Suzuki-type fixed point results in metric type spaces. Fixed Point Theory Appl. 2012 (2012), doi:10.1186/1687-1812-2012-126.

  8. N. Hussain, E. Karapınar, P. Salimi and F. Akbar, \({\alpha}\)-admissible mappings and related fixed point theorems. J. Inequal. Appl. 2013 (2013), doi:10.1186/1029-242X-2013-114.

  9. N. Hussain, M. A. Kutbi and P. Salimi, Fixed point theory in \({\alpha}\) -complete metric spaces with applications. Abstr. Appl. Anal. 2014 (2014), Article ID 280817, 11 pages.

  10. N. Hussain, M. A. Kutbi, S. Khaleghizadeh and P. Salimi, Discussions on recent results for \({\alpha}\)-\({\psi}\) -contractive mappings. Abstr. Appl. Anal. 2014 (2014), Article ID 456482, 13 pages.

  11. N. Hussain, A. Latif and I. Iqbal, Fixed point results for generalized Fcontractions in modular metric and fuzzy metric spaces. Fixed Point Theory Appl. 2015 (2015), doi:10.1186/s13663-015-0407-1.

  12. Hussain N., Salimi P.: Suzuki-Wardowski type fixed point theorems for \({\alpha}\)- GF-contractions. Taiwanese J. Math. 18, 1879–1895 (2014)

    Article  MathSciNet  Google Scholar 

  13. M. A. Kutbi, N. Hussain and S. Khaleghizadeh, New PPF dependent fixed point theorems for Suzuki type GF-contractions. J. Funct. Spaces 2015 (2015), Article ID 136306, 13 pages.

  14. Nieto J.J., Rodríguez-López R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order 22, 223–229 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  15. P. Salimi, A. Latif and N. Hussain, Modified \({\alpha}\)-\({\psi}\) -contractive mappings with applications. Fixed Point Theory Appl. 2013 (2013), doi:10.1186/1687-1812-2013-151.

  16. Samet B., Vetro C., Vetro P.: Fixed point theorems for \({\alpha}\)-\({\psi}\)-contractive type mappings. Nonlinear Anal. 75, 2154–2165 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  17. Suzuki T.: A generalized Banach contraction principle that characterizes metric completeness. Proc. Amer. Math. Soc. 136, 1861–1869 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Suzuki T.: A new type of fixed point theorem in metric spaces. Nonlinear Anal. 71, 5313–5317 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran

    Vahid Parvaneh

  2. Department of Mathematics, Sanandaj Branch, Islamic Azad University, Sanandaj, Iran

    Farhan Golkarmanesh

  3. Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Nawab Hussain

  4. Department of Mathematics, Payame Noor University, Tehran, Iran

    Peyman Salimi

Authors
  1. Vahid Parvaneh
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  2. Farhan Golkarmanesh
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  3. Nawab Hussain
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  4. Peyman Salimi
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Correspondence to Vahid Parvaneh.

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Parvaneh, V., Golkarmanesh, F., Hussain, N. et al. New fixed point theorems for \({\alpha}\)-\({H\Theta}\)-contractions in ordered metric spaces. J. Fixed Point Theory Appl. 18, 905–925 (2016). https://doi.org/10.1007/s11784-016-0330-z

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  • DOI: https://doi.org/10.1007/s11784-016-0330-z

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