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Extension of almost generalized weakly contractive mappings in rectangular b-metric spaces and fixed point results

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Abstract

In this work, we extend the concept of an almost generalized weakly contractive mapping in rectangular b-metric spaces. The establish of fixed point of such mappings is also provided. We give an example to support our results.

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References

  1. An, T.V., Dung, N.V., Kadelburg, Z., Radenović, S.: Various generalizations of metric spaces and fixed point theorems. Rev Real Acad Cienc Exact Fis Nat Ser A Mat 109, 175–198 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  2. Arshad, M., Ameer, E., Karapinar, E.: Generalized contractions with triangular alpha-orbital admissible mapping on Branciari metric spaces. J. Inequal. Appl. 2016, 63 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  3. Berinde, V.: Approximating fixed points of weak contractions using the Picard iteration. Nonlinear Anal. Forum 9, 43–53 (2004)

    MathSciNet  MATH  Google Scholar 

  4. Berinde, V.: General constructive fixed point theorems for Ćirić-type almost contractions in metric spaces. Carpathian J. Math. 24, 10–19 (2008)

    MathSciNet  MATH  Google Scholar 

  5. Branciari, A.: A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces. Publ. Math. Debr. 57, 31–37 (2000)

    MathSciNet  MATH  Google Scholar 

  6. Czerwik, S.: Contraction mappings in \(b\)-metric spaces. Acta Math. Inf. Univ. Ostrav. 1, 5–11 (1993)

    MathSciNet  MATH  Google Scholar 

  7. Czerwik, S.: Nonlinear set-valued contraction mappings in \(b\)-metric spaces. Atti Sem. Mat. Fis. Univ. Modena 46, 263–276 (1998)

    MathSciNet  MATH  Google Scholar 

  8. Erhan, I.M., Karapinar, E., Sekulić, T.: Fixed points of \((\psi, \varphi )\) contractions on rectangular metric spaces. Fixed Point Theory Appl. 2012, 138 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hussain, N., Parvaneh, V., Roshan, J.R., Kadelburg, Z.: Fixed points of cyclic \((\psi, \varphi, L, A, B)\)-contractive mappings in ordered \(b\)-metric spaces with applications. Fixed Point Theory Appl. 2013, 256 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. Jleli, M., Samet, B., A new generalization of the Banach contraction principle. J. Inequal. Appl. 2014, Article ID 38 (2014)

  11. Khan, M.S., Swaleh, M., Sessa, S.: Fixed point theorems by altering distances between the points. Bull. Aust. Math. Soc. 30, 1–9 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  12. Lakzian, H., Samet, B.: Fixed points for \((\psi, \varphi )\)-weakly contractive mapping in generalized metric spaces. Appl. Math. Lett. 25, 902–906 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Popescu, O.: Some new fixed point theorems for a-geraghty contraction type maps in metric spaces. Fixed Point Theory Appl. 2014, Article ID 190 (2014)

  14. Roshan, J.R., Hussain, N., Parvaneh, V., Kadelburg, Z.: New fixed point results in rectangular b-metric spaces. Nonlinear Anal. Model. Control 21, 614–634 (2016)

    Article  MathSciNet  Google Scholar 

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Acknowledgments

The P. Sookprasert would like to thank the Faculty of Science, KMUTT for financial support during the preparation of this manuscript for the Ph.D. Program at KMUTT. Moreover, P. Kumam and D. Thongtha would like to thank Theoretical and Computational Science Center (TaCS).

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Correspondence to Poom Kumam.

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Sookprasert, P., Kumam, P., Thongtha, D. et al. Extension of almost generalized weakly contractive mappings in rectangular b-metric spaces and fixed point results. Afr. Mat. 28, 271–278 (2017). https://doi.org/10.1007/s13370-016-0443-y

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  • DOI: https://doi.org/10.1007/s13370-016-0443-y

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