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Coupled fixed point theorems in partially ordered metric spaces via mixed g-monotone property

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Abstract

In this paper we study some coupled fixed point theorems and coupled coincidence fixed point theorems for infinite family mappings satisfying different contractive conditions on the complete partially ordered metric space with the help of concept of mixed g-monotone property. Further we used generalized Darbo type coupled fixed point theorem to find the existence of solutions for a system of nonlinear functional integral equations in Banach space with the help of measure of noncompactness.

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References

  1. Abbas, M., Ali Khan, M., Radenović, S.: Common coupled fixed point theorems in cone metric spaces for \(w\)-compatible mappings. Appl. Math. Comput. 217, 195–202 (2010)

    MathSciNet  MATH  Google Scholar 

  2. Agarwal, R.P., Sintunavarat, W., Kumam, P.: Coupled coincidence point and common coupled fixed point theorems lacking the mixed monotone property. Fixed Point Theory Appl. 2013, 22 (2013)

    Article  MathSciNet  Google Scholar 

  3. Arab, R., Rabbani, M.: Coupled coincidence and common fixed point theorems for mappings in partially ordered metric spaces. Math. Sci. Lett. 3(2), 81–87 (2014)

    Article  Google Scholar 

  4. Arab, R.: A common coupled fixed point theorem for two pairs of \(w\)-compatible mappings in \(G\)-metric spaces. Sohag J. Math. 1(1), 37–43 (2014)

    Google Scholar 

  5. Arab, R.: Coupled coincidence point results on partial metric spaces. Sohag J. Math. 2(1), 23–28 (2015)

    MathSciNet  Google Scholar 

  6. Arab, R., Allahyari, R., Haghighi, A.S.: Existence of solutions of infinite systems of integral equations in two variables via measure of noncompactness. Appl. Math. Comput. 246, 283–291 (2014)

    MathSciNet  MATH  Google Scholar 

  7. Banaś, J., Goebel, K.: Measure of Noncompactness in Banach Spaces. Lecture Notes in Pure and Applied Mathematics, vol. 60. Marcel Dekker, New York (1980)

    MATH  Google Scholar 

  8. Berinde, V.: Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces. Nonlinear Anal. TMA 74(18), 7347–7355 (2011)

    Article  MathSciNet  Google Scholar 

  9. Bhaskar, T.G., Lakshmikantham, V.: Fixed point theory in partially ordered metric spaces and applications. Nonlinear Anal. 65, 1379–1393 (2006)

    Article  MathSciNet  Google Scholar 

  10. Choudhury, B.S., Kundu, A.: A coupled coincidence point result in partially ordered metric spaces for compatible mappings. Nonlinear Anal. 73, 2524–2531 (2010)

    Article  MathSciNet  Google Scholar 

  11. Choudhury, B.S., Metiya, N., Kundu, A.: Coupled coincidence point theorems in ordered metric spaces. Ann. Univ. Ferrara 57, 1–16 (2011)

    Article  MathSciNet  Google Scholar 

  12. A.Das, B. Hazarika, R. Arab, M. Mursaleen, Applications of a fixed point theorem to the existence of solutions to the nonlinear functional integral equations in two variables, Rend. Circ. Mat. Palermo, II. Ser, https://doi.org/10.1007/s12215-018-0347-9

  13. Jungck, G.: Commuting mappings and fixed points. Am. Math. Mon. 83, 261–263 (1976)

    Article  MathSciNet  Google Scholar 

  14. Jungck, G.: Compatible mappings and common fixed points. Int. J. Math. Math. Sci. 9, 771–779 (1986)

    Article  MathSciNet  Google Scholar 

  15. Lakshmikantham, V., Ćirić, L.: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal. TMA 70(12), 4341–4349 (2009)

    Article  MathSciNet  Google Scholar 

  16. Luong, N.V., Thuan, N.X.: Coupled fixed point theorems in partially ordered metric spaces. Bul. Math. Anal. Appl. 4, 16–24 (2010)

    MathSciNet  MATH  Google Scholar 

  17. Shatanawi, W., Samet, B., Abbas, M.: Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces. Math. Comput. Model. 55(34), 680–687 (2012)

    Article  MathSciNet  Google Scholar 

  18. Tasković, M.R.: Axiom of Infinite choice, transversal ordered spring spaces and fixed points. Fixed Point Theory Appl. 2018, 10 (2018). (32 pages)

    Article  MathSciNet  Google Scholar 

  19. Petrusel, A., Petruśel, G., Xiao, Yi-bin, Yao, Jen-Chih: Fixed point theorems for generalized contractions with applications to coupled fixed point theory. J. Nonlinear Convex Anal. 19(1), 71–81 (2018)

    MathSciNet  MATH  Google Scholar 

  20. Ran, A.C.M., Reurings, M.C.B.: A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Amer. Math. Soc. 132, 1435–1443 (2004)

    Article  MathSciNet  Google Scholar 

  21. Nieto, J.J., Rodrguez-López, R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order 22, 223–239 (2005)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors acknowledge the financial support provided by King Mongkut’s University of Technology Thonburi through the“KMUTT 55th Anniversary Commemorative Fund”. This project was supported by the Theoretical and Computational Science (TaCS) Center under Computational and Applied Science for Smart Innovation Cluster (CLASSIC), Faculty of Science, KMUTT.

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Authors and Affiliations

  1. Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh, Arunachal Pradesh, 791112, India

    Bipan Hazarika

  2. Department of Mathematics, Gauhati University, Guwahati, Assam, 781014, India

    Bipan Hazarika

  3. Department of Mathematics, Sari Branch, Islamic Azad University, Sari, 19318, Iran

    Reza Arab

  4. KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok, 10140, Thailand

    Poom Kumam

  5. KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok, 10140, Thailand

    Poom Kumam

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  1. Bipan Hazarika
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  2. Reza Arab
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  3. Poom Kumam
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Correspondence to Bipan Hazarika.

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Hazarika, B., Arab, R. & Kumam, P. Coupled fixed point theorems in partially ordered metric spaces via mixed g-monotone property. J. Fixed Point Theory Appl. 21, 1 (2019). https://doi.org/10.1007/s11784-018-0638-y

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  • DOI: https://doi.org/10.1007/s11784-018-0638-y

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