Existence and uniqueness of the solutions of some classes of integral equations C*-algebra-valued b-metric spaces
Abstract
Introduction/purpose: The aim of the paper is to establish some coupled fixed
point results in C*-algebra-valued b-metric spaces. Moreover, the obtained results
are used to define the sufficient conditions for the existence of the solutions
of some classes of integral equations.
Methods: The method of coupled fixed points gives the sufficient conditions for
the existence of the solution of some classes of integral equations.
Results: New results were obtained on coupled fixed points in C * -algebra-valued
b-metric space.
Conclusion: The obtained results represent a contribution in the fixed point theory
and open new possibilities of application in the theory of differential and integral
equations.
References
Ali Abou Bakr, S. M. 2019. Common fixed point of generalized cyclic Banach algebra contractions and Banach algebra Kannan types of mappings on cone quasi metric spaces. Journal of Nonlinear Sciences and Applications (JNSA), 12(10), pp.644-655. Available at: http://dx.doi.org/10.22436/jnsa.012.10.03.
Bai, C. 2016. Coupled fixed point theorems in C*-algebra-valued b-metric spaces with application. Fixed Point Theory and Applications, art.number:70. Available at: https://doi.org/10.1186/s13663-016-0560-1.
Bonsal, F.F. 1962. Lectures On Some Fixed Point Theorems Of Functional Analysis. Bombay, India: Tata Institute Of Fundamental Research [online]. Available at: http://www.math.tifr.res.in/~publ/ln/tifr26.pdf. [Accessed: 25 September 2020].
Cao, T. and Xin, Q. 2016. Common coupled fixed point theorems in C*-algebra-valued metric spaces. arXiv:1601.07168v1[math.OA], 26 January [online]. Available at: https://arxiv.org/abs/1601.07168 [Accessed: 25 September 2020].
Huang, H., Došenović, T. and Radenović, S. 2018. Some fixed point results in b-metric spaces approach to the existence of a solution to nonlinear integral equations. Journal of Fixed Point Theory and Applications, 20(art.number:105). Available at: https://doi.org/10.1007/s11784-018-0577-7.
Hussain, A., Kanwal, T., Mitrović, Z. D. and Radenović, S., 2018. Optimal Solutions and Applications to Nonlinear Matrix and Integral Equations via Simulation Function. Filomat, 32(17), pp.6087-6106. Available at: https://doi.org/10.2298/FIL1817087H.
Hussain, N. and Mitrović, Z. D. 2017. On multi-valued weak quasi-contractions in b-metric spaces. Journal of Nonlinear Sciences and Applications (JNSA), 10(7), pp.3815-3823. Available at: http://dx.doi.org/10.22436/jnsa.010.07.35.
Kadelburg, Z., Nastasi, A., Radenović, S. and Vetro, P. 2016. Fixed points of contractions and cyclic contractions on C*-algebra-valued b-metric spaces. Advances in Operator Theory, 1(1), pp.92-103. Available at: https://doi.org/10.22034/aot.1610.1030.
Kadelburg, Z. and Radenović, S., 2016. Fixed point results in C*-algebravalued metric spaces are direct consequences of their standard metric counterparts. Fixed Point Theory and Applications, art.number:53(2016). Available at: https://doi.org/10.1186/s13663-016-0544-1.
Kongban, C. and Kumam, P. 2018. Quadruple random common fixed point results of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras. Journal of Nonlinear Sciences and Applications (JNSA), 11(1), pp.131-149. Available at: http://dx.doi.org/10.22436/jnsa.011.01.10.
Ma, Z. and Jiang, L. 2015. C*-Algebra-valued b-metric spaces and related fixed point theorems. Fixed Point Theory and Applications , art.number:222(2015). Available at: https://doi.org/10.1186/s13663-015-0471-6.
Ma, Z.H., Jiang, N. and Sun, H.K. 2014. C*-Algebra-valued metric spaces and related fixed point theorems. Fixed Point Theory and Applications, art.number:206(2014). Available at: https://doi.org/10.1186/1687-1812-2014-206.
Mitrović, Z.D., Aydi, H., Md Noorani, M.S. and Qawaqneh, H. 2019. The weight inequalities on Reich type theorem in b-metric spaces. Journal of Mathematics and Computer Science (JMCS), 19(1), pp.51–57. Available at: http://dx.doi.org/10.22436/jmcs.019.01.07.
Radenović, S., Vetro, P., Nastasi, A. and Quan, L.T. 2017. Coupled fixed point theorems in C*-algebra-valued b-metric spaces. Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics, 9(1), pp.81-90. Available at: https://doi.org/10.5937/SPSUNP1701081R.
Radenović, S., Zoto, K., Dedović, N., Šešum Čavić, V. and Ansari, A.H. 2019. Bhaskar-Guo-Lakshmikantam-Ćirić type results via new functions with applications to integral equations. Applied Mathematics and Computation, 357(C), pp.75-87. Available at: https://doi.org/10.1016/j.amc.2019.03.057.
Todorčević, V. 2019. Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics. Springer Nature Switzerland AG. ISBN: 978-3-030-22591-9.
Vujaković, J., Kishore, G.N.V., Rao, K.P.R., Radenović, S. and Sadik, S.K. 2019. Existence and Unique Coupled Solution in Sb-Metric Spaces by Rational Contraction with Application. Mathematics, 7(4), p.313. Available at: https://doi.org/10.3390/math7040313.
Zoto, K., Rhoades, B.E. and Radenović, S. 2019. Common fixed point theorems for a class of (s; q)-contractive mappings in b-metric-like spaces and applications to integral equations. Mathematica Slovaca, 69(1), pp.233-247. Available at: https://doi.org/10.1515/ms-2017-0217.
Wu, X. and Zhao, L. 2019. Fixed point theorems for generalized α-ψ type contractive mappings in b-metric spaces and applications,. Journal of Mathematics and Computer Science (JMCS), 18(1), pp.49–62. Available at: http://dx.doi.org/10.22436/jmcs.018.01.06.
Proposed Creative Commons Copyright Notices
Proposed Policy for Military Technical Courier (Journals That Offer Open Access)
Authors who publish with this journal agree to the following terms:
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).