×

Pata type contractions involving rational expressions with an application to integral equations. (English) Zbl 1469.54128

Summary: 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.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
54E50 Complete metric spaces
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] T. Abdeljawad, R. P. Agarwal, E. Karapinar and P. Sumati Kumari, Solutions of the nonlinear integral equation and fractional differential equation using the technique of a fixed point with a numerical experiment in extended b-metric space, Symmetry, 11 (2019), Article Number 686. · Zbl 1425.47016
[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. · Zbl 1459.34180
[3] A. Atangana, Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties, Phys. A, 505, 688-706 (2018) · Zbl 1514.34009
[4] A. Atangana; T. Mekkaoui, Trinition the complex number with two imaginary parts: Fractal, chaos and fractional calculus, Chaos Solitons Fractals, 128, 366-381 (2019) · Zbl 1483.39008
[5] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3, 133-181 (1922) · JFM 48.0201.01
[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. · Zbl 1499.39073
[7] F. Jarad; T. Abdeljawad; Z. Hammouch, On a class of ordinary differential equations in the frame of Atangana-Baleanu fractional derivative, Chaos Solitons Fractals, 117, 16-20 (2018) · Zbl 1442.34016
[8] Z. Kadelburg; S. Radenović, Fixed point theorems under Pata-type conditions in metric spaces, J. Egyptian Math. Soc., 24, 77-82 (2016) · Zbl 1337.54040
[9] Z. Kadelburg; S. Radenović, A note on Pata-type cyclic contractions, Sarajevo J. Math., 11, 235-245 (2015) · Zbl 1336.54046
[10] Z. Kadelburg; S. Radenović, Pata-type common fixed point results in b-metric and \(\begin{document}b\end{document} \)-rectangular metric spaces, J. Nonlinear Sci. Appl., 8, 944-954 (2015) · Zbl 1437.54054
[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. · Zbl 1399.54123
[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. · Zbl 1487.54065
[13] E. Karapinar, I. M. Erhan and Ü. Aksoy, Weak \(\begin{document} \psi \end{document} \)-contractions on partially ordered metric spaces and applications to boundary value problems, Bound. Value Probl., 2014 (2014), 149, 15 pp. · Zbl 1432.54063
[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, 16-35 (1837)
[15] V. Pata, A fixed point theorem in metric spaces, J. Fixed Point Theory Appl., 10, 299-305 (2011) · Zbl 1264.54065
[16] O. Popescu, Some new fixed point theorems for \(\begin{document} \alpha \end{document} \)-Geraghty contractive type maps in metric spaces, Fixed Point Theory Appl., 2014 (2014), 12 pp. · Zbl 1451.54020
[17] T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71, 5313-5317 (2009) · Zbl 1179.54071
[18] T. Suzuki, A generalized Banach contraction principle which characterizes metric completeness, Proc. Amer. Math. Soc., 136, 1861-1869 (2008) · Zbl 1145.54026
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.