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Pata type contractions involving rational expressions with an application to integral equations

  • * Corresponding author: Erdal Karapınar

    * Corresponding author: Erdal Karapınar 
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  • In this paper, we introduce the notion of rational Pata type contraction in the complete metric space. After discussing the existence and uniqueness of a fixed point for such contraction, we consider a solution for integral equations.

    Mathematics Subject Classification: Primary: 54H25, 47H10; Secondary: 54E50.


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    [2] A. Ali, K. Shah, F. Jarad, V. Gupta and T. Abdeljawad, Existence and stability analysis to a coupled system of implicit type impulsive boundary value problems of fractional-order differential equations, Adv. Difference Equ., (2019), Article Number 101, 21 pp. doi: 10.1186/s13662-019-2047-y.
    [3] A. Atangana, Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties, Phys. A, 505 (2018), 688-706.  doi: 10.1016/j.physa.2018.03.056.
    [4] A. Atangana and T. Mekkaoui, Trinition the complex number with two imaginary parts: Fractal, chaos and fractional calculus, Chaos Solitons Fractals, 128 (2019), 366-381.  doi: 10.1016/j.chaos.2019.08.018.
    [5] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133-181.  doi: 10.4064/fm-3-1-133-181.
    [6] R. I. Batt, T. Abdeljawad, M. A.Alqudah and Mujeeb ur Rehman, Ulam stability of Caputo q-fractional delay difference equation: q-fractional Gronwall inequality approach, J. Inequal. Appl., 2019 (2019), 305. doi: 10.1186/s13660-019-2257-6.
    [7] F. JaradT. Abdeljawad and Z. Hammouch, On a class of ordinary differential equations in the frame of Atangana-Baleanu fractional derivative, Chaos Solitons Fractals, 117 (2018), 16-20.  doi: 10.1016/j.chaos.2018.10.006.
    [8] Z. Kadelburg and S. Radenović, Fixed point theorems under Pata-type conditions in metric spaces, J. Egyptian Math. Soc., 24 (2016), 77-82.  doi: 10.1016/j.joems.2014.09.001.
    [9] Z. Kadelburg and S. Radenović, A note on Pata-type cyclic contractions, Sarajevo J. Math., 11 (2015), 235-245. 
    [10] Z. Kadelburg and S. Radenović, Pata-type common fixed point results in b-metric and $b$-rectangular metric spaces, J. Nonlinear Sci. Appl., 8 (2015), 944-954.  doi: 10.22436/jnsa.008.06.05.
    [11] Z. Kadelburg and S. Radenovic, Fixed point and tripled fixed point theprems under Pata-type conditions in ordered metric spaces, International Journal of Analysis and Applications, 6, (2014), 113–122.
    [12] E. Karapinar, T. Abdeljawad and F. Jarad, Applying new fixed point theorems on fractional and ordinary differential equations, Adv. Difference Equ., 2019 (2019), Paper No. 421, 25 pp. doi: 10.1186/s13662-019-2354-3.
    [13] E. Karapinar, I. M. Erhan and Ü. Aksoy, Weak $\psi$-contractions on partially ordered metric spaces and applications to boundary value problems, Bound. Value Probl., 2014 (2014), 149, 15 pp. doi: 10.1186/s13661-014-0149-8.
    [14] J. Liouville, Second mémoire sur le développement des fonctions ou parties de fonctions en séries dont divers termes sont assujettis á satisfaire a une m eme équation différentielle du second ordre contenant un paramétre variable, J. Math. Pure et Appi., 2 (1837), 16-35. 
    [15] S. K. PandaT. Abdeljawad and  C. RavichandranNovel fixed point approach to Atangana-Baleanu fractional and -Fredholm integral equations, Alexandria Engineering Journal, in press, 2020.  doi: 10.1016/j.aej.2019.12.027.
    [16] S. K. PandaT. Abdeljawad and  K. K. SwamyNew numerical scheme for solving integral equations via fixed point method using distinct $\omega-F$-contractions, Alexandria Engineering Journal, in press, 2020.  doi: 10.1016/j.aej.2019.12.034.
    [17] V. Pata, A fixed point theorem in metric spaces, J. Fixed Point Theory Appl., 10 (2011), 299-305.  doi: 10.1007/s11784-011-0060-1.
    [18] O. Popescu, Some new fixed point theorems for $\alpha$-Geraghty contractive type maps in metric spaces, Fixed Point Theory Appl., 2014 (2014), 12 pp. doi: 10.1186/1687-1812-2014-190.
    [19] T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313-5317.  doi: 10.1016/j.na.2009.04.017.
    [20] T. Suzuki, A generalized Banach contraction principle which characterizes metric completeness, Proc. Amer. Math. Soc., 136 (2008), 1861-1869.  doi: 10.1090/S0002-9939-07-09055-7.
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