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Quadruple Fixed Point Theorem for Partially Ordered Metric Space with Application to Integral Equations

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Mathematics and Computing (ICMC 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 253))

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Abstract

In this paper, two theorems have been established. The first theorem says the existences of a quadruple fixed point theorem in partially ordered metric space for nonlinear contraction mapping which is \((\alpha )\)-admissible and satisfies the mixed monotone property. The second result is proved for non-continuous mapping in addition to some other conditions. A suitable example of nonlinear contraction mapping validates the result. Moreover, an application to the integral equation is also presented.

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References

  1. Arvanitakis, A.D.: A proof of the generalized Banach contraction conjecture. Proc. Am. Math. Soc. 131(12), 36473656 (2003)

    Article  MathSciNet  Google Scholar 

  2. Choudhury, B.S., Das, K.P.: A new contraction principle in Menger spaces. Acta Math. Sin. 24(8), 13791386 (2008)

    Article  MathSciNet  Google Scholar 

  3. Boyd, D.W., Wong, J.S.W.: On nonlinear contractions. Proc. Am. Math. Soc. 20, 458464 (1969)

    Article  MathSciNet  Google Scholar 

  4. Aydi, H., Vetro, C., Sintunavarat, W., Kumam, P.: Coincidence and fixed points for contractions and cyclical contractions in partial metric spaces. Fixed Point Theory Appl. 2012, 124 (2012)

    Article  MathSciNet  Google Scholar 

  5. Lakshmikantham, V., Ciric, LjB: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal. 70, 4341–4349 (2009)

    Article  MathSciNet  Google Scholar 

  6. Sintunavarat, W., Kumam, P.: Weak condition for generalized multi-valued (f,)-weak contraction mappings. Appl. Math. Lett. 24, 460465 (2011)

    Article  MathSciNet  Google Scholar 

  7. Sintunavarat, W., Kumam, P.: Common fixed point theorem for cyclic generalized multi-valued contraction mappings. Appl. Math. Lett. 25(11), 18491855 (2012)

    Article  MathSciNet  Google Scholar 

  8. Sintunavarat, W., Cho, Y.J., Kumam, P.: Common fixed point theorems for c-distance in ordered cone metric spaces. Comput. Math. Appl. 62, 19691978 (2011)

    Article  MathSciNet  Google Scholar 

  9. Ran, A.C.M., Reurings, M.C.B.: A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Am. Math. Soc. 132, 14351443 (2004)

    Article  MathSciNet  Google Scholar 

  10. Bhaskar, T.G., Lakshmikantham, V.: Fixed point theory in partially ordered metric spaces and applications. Nonlinear Anal. 65, 13791393 (2006)

    Article  Google Scholar 

  11. Nieto, J.J., Rodriguez-Lopez, R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order 22, 223239 (2005)

    Article  MathSciNet  Google Scholar 

  12. Nieto, J.J., Lopez, R.R.: Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations. Acta Math. Sin. Engl. Ser. 23(12), 2205–2212 (2007)

    Article  MathSciNet  Google Scholar 

  13. Agarwal, R.P., El-Gebeily, M.A., ORegan D.: Generalized contractions in partially ordered metric spaces. Appl. Anal. 87, 18 (2008)

    Article  MathSciNet  Google Scholar 

  14. Choudhury, B.S., Metiya, N., Kundu, A.: Coupled coincidence point theorems in ordered metric spaces. Ann. Univ. Ferrara. 57, 116 (2011)

    Article  MathSciNet  Google Scholar 

  15. Karapnar, E.: Couple fixed point on cone metric spaces. Gazi Univ. J. Sci. 24, 51–58 (2011)

    Google Scholar 

  16. Karapnar, E.: Coupled fixed point theorems for nonlinear contractions in cone metric spaces. Comput. Math. Appl. 59, 36563668 (2010)

    MathSciNet  Google Scholar 

  17. Aydi, H.: Some coupled fixed point results on partial metric spaces. Int. J. Math. Math. Sci. 2011, Article ID 647091, 11 pages (2011)

    Google Scholar 

  18. Abbas, M., Khan, M.A., Radenovic, S.: Common coupled fixed point theorem in cone metric space for wcompatible mappings. Appl. Math. Comput. 217, 195202 (2010)

    Google Scholar 

  19. Luong, N.V., Thuan, N.X.: Coupled fixed points in partially ordered metric spaces and application. Nonlinear Anal. 74, 983992 (2011)

    Article  MathSciNet  Google Scholar 

  20. Berinde, V., Borcut, M.: Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces. Nonlinear Anal. 74, 48894897 (2011)

    MathSciNet  MATH  Google Scholar 

  21. Samet, B., Vetro, C.: Coupled fixed point, f-invariant set and fixed point of N-order. Ann. Funct. Anal. 1(2), 4656 (2010)

    Article  MathSciNet  Google Scholar 

  22. Karapnar, E.: Quartet fixed point for nonlinear contraction. http://arxiv.org/abs/1106.5472 (27 Jun 2011)

  23. Karapnar, E.: A new quartet fixed point theorem for nonlinear contractions. J. Fixed Point Theory Appl. 6(2), pp. 119–135 (2011)

    Google Scholar 

  24. Karapnar, E.: Quadruple fixed point theorems for weak \(\phi \)-contractions. ISRN Math. Anal. 2011, Article ID 989423, 15 pages (2011)

    Google Scholar 

  25. Karapnar, E., Luong, N.V.: Quadruple fixed point theorems for nonlinear contractions. Comput. Math. Appl. 64, 18391848 (2012)

    MathSciNet  Google Scholar 

  26. Karapnar, E., Berinde, V.: Quadruple fixed point theorems for nonlinear contractions in partially ordered metric spaces. Banach J. Math. Anal. 6(1), 7489 (2012)

    MathSciNet  Google Scholar 

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Acknowledgements

The authors are thankful to the affiliated college authorities for financial support given by them.

Author information

Authors and Affiliations

  1. Department of Mathematics, Yeshwantrao Chavan College of Engineering, Nagpur, India

    Manjusha P. Gandhi

  2. Department of Mathematics, Rajiv Gandhi College of Engineering and Research, Nagpur, India

    Anushri A. Aserkar

Authors
  1. Manjusha P. Gandhi
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  2. Anushri A. Aserkar
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Corresponding author

Correspondence to Manjusha P. Gandhi .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh, India

    Debdas Ghosh

  2. Department of Computer Science and Engineering, Haldia Institute of Technology, Haldia, West Bengal, India

    Debasis Giri

  3. Department of Mathematics, University of Central Florida, Orlando, FL, USA

    Ram N. Mohapatra

  4. Faculty of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan

    Kouichi Sakurai

  5. UÅŸak University, UÅŸak, Turkey

    Ekrem Savas

  6. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh, India

    Tanmoy Som

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Gandhi, M.P., Aserkar, A.A. (2018). Quadruple Fixed Point Theorem for Partially Ordered Metric Space with Application to Integral Equations. In: Ghosh, D., Giri, D., Mohapatra, R., Sakurai, K., Savas, E., Som, T. (eds) Mathematics and Computing. ICMC 2018. Springer Proceedings in Mathematics & Statistics, vol 253. Springer, Singapore. https://doi.org/10.1007/978-981-13-2095-8_14

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