Kontraktivni uslovi u b-metričkim prostorima

  • Tatjana M. Došenović University of Novi Sad, Faculty of Technology
  • Mirjana V. Pavlović University of Kragujevac, Faculty of Sciences, Department of Mathematics and Informatics
  • Stojan N. Radenović University of Belgrade, Faculty of Mechanical Engineering
Ključne reči: metric space||, ||metrički prostor, common fixed point||, ||zajednička fiksna tačka, altering distance function||, ||funkcija promene razdaljine, point of coincidence||, ||tačka koincidencije, weak compatibility||, ||slaba kompatibilnost,

Sažetak


Cilj ovog rada jeste da razmotri razne kontraktivne uslove u b-metričkim prostorima koji su nedavno objavljeni. Naši rezultati popravljaju i dopunjuju mnoge nedavne rezultate iz ovog konteksta. Koristeći nedavno dobijeni rezultat R. Mikuleskua i A. Mihaila (Miculescu & Michail, 2017, pp.1-11),  autori ovog članka pokazuju da dokazi mnogih poznatih rezultata u kontekstu b-metričkih prostora mogu biti dosta skraćeni.

Reference

Abbas, M., Chema, I.Z., Razani, A., 2016. Existence of common fixed point for b-metric rational type contraction. Filomat, 30(6), pp.1413-1429. Available at: http://dx.doi.org/10.2298/FIL1606413A.

Aghajani, A., Abbas, M., Roshan, J.R., 2014. Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces. Math. Slovaca, 64(4), pp.941-960. Available at: https://doi.org/10.2478/s12175-014-0250-6

Allahyar, R., Arab, R., Haghighi, A.S., 2014. A generalization on weak contractions in partially ordered b-metric spaces and its application to quadratic integral equations. J. Inequal. Appl., 2014:355. Available at: https://doi.org/10.1186/1029-242X-2014-355.

Ansari, A., Razani, A., Hussain, N., 2017. Fixed and coincidence points for hybrid rational Geraghty contractive mappings in ordered b-metric spaces. Int. J. Nonlinear Anal. Appl., 8(1), pp.315-329. Available at: http://ijnaa.semnan.ac.ir/article_453.html.

Banach, S., 1922. Sur les opérations dans les ensembles abstraits et leur application aux équations integrals. Fundamenta Mathematicae, 3(1), pp.133-181.

Bakhtin, I.A., 1989. The contraction principle in quasimetric spaces. Funct. Anal., 30, pp.26-37.

Chandok, S., Huang, H., Radenović, S., 2017a. Some fixed point results for generalized F-Suzuki type contractions in b-metric spaces, to appear in Sahad Comunications in Mathematical Analysis.

Chandok, S.C., Jovanović, M.S., Radenović, S.N., 2017b. Ordered b-metric spaces and Geraghty type contractive mappings. Vojnotehnicki glasnik/Military Technical Courier, 65(2), pp.331–345. Available at: http://dx.doi.org/10.5937/vojtehg65-13266.

Czerwik, S., 1993. Contraction mappings in-metric spaces. Acta Math. Inform. Univ. Ostrav, 1, pp.5-11.

Demma, M. & Vetro, P., 2015. Picard sequence and fixed point results on b-metric spaces. J. Funct. Space, Vol.2015. Available at: http://dx.doi.org/10.1155/2015/189861.

Ding, H.S., Imdad, M., Radenović, S., Vujaković, J., 2016. On some fixed point results in b-metric, rectangular and b-rectangular metric spaces. Arab J. Math. Sci, 22(2), pp.151-164. Available at: https://doi.org/10.1016/j.ajmsc.2015.05.003.

Dung, N.V. & Hang, V.T.L., 2016. On relaxions of contraction constants and Caristi’s theorem in b-metric spaces. J. Fixed Point Theory Appl., 18(2), pp.267-284. Available at: https://doi.org/10.1007/s11784-015-0273-9.

Harandi, A.A., 2014. Fixed point theory for quasi-contraction maps in b-metric spaces. Fixed Point Theory, 15(2), pp.351-358. Available at: http://www.math.ubbcluj.ro/~nodeacj/vol__15(2014)_no_2.php

Huang, H., Radenović, S., Vujaković, J., 2015. On some recent coincidence and immediate consequences in partially ordered b-metric spaces. Fixed Point Theory Appl., 2015:63. Available at: https://doi.org/10.1186/s13663-015-0308-3.

Jeong, G.S. & Rhoades, B.E., 2005, Maps for which Fixed Point Theory Appl., 6, 71-105, Available at: https://www.novapublishers.com/catalog/product_info.php?products_id=4068.

Jovanović, M., 2016. Contribution to the theory of abstract metric spaces, Ph.D. thesis, University of Belgrade, Faculty of Mathematics, Belgrade. Available at: http://nardus.mpn.gov.rs/handle/123456789/7975.

Kaushik, P., Kumar, S., Tas, K., 2017. A new class of contraction in b-metric spaes and applications. Abstr. Appl. Anal., Vol.2017. Available at: https://doi.org/10.1155/2017/9718535.

Khamsi, M. A. & Hussain, N., 2010. KKM mappings in metric type spaces. Nonlinear Anal., 73(9), pp.3123-3129. Available at: https://doi.org/10.1016/j.na.2010.06.084.

Khan, M. S., Swaleh, M., Sessa, S., 1984. Fixed point theorems by altering distances between the points. Bul. Aust. Math. Soc., 30(1), pp.1-9. Available at: https://doi.org/10.1017/S0004972700001659.

Kir, M. & Kiziltunc, H., 2013. On Some Well Known Fixed Point Theorems in b-Metric Spaces. Turkish J. Anal. Numb. Theory, 1(1), pp.13-16. Available at: http://dx.doi.org/10.12691/tjant-1-1-4.

Kumam, P., Sintunavarat, W., Sedghi, S., Shobkolaei, N., 2015. Common fixed point of two R-weakly commuting mappings in b-metric spaces. J. Funct. Space, Vol.2015. Available at: http://dx.doi.org/10.1155/2015/350840.

Latif, A., Parvaneh, V., Salimi, P., Al-Mazrooei, A.E., 2015. Various Suzuki type theorems in b-metric spaces. J. Nonlinear Sci. Appl. 8(4), pp.363-377.

Liu, L. & Gu, F., 2016. Common fixed point theorems for six self-maps in b-metric spaces with nonlinear contractive conditions. J. Nonlinear Sci. Appl., 9(12), pp.5909-5930.

Miculescu, R. & Mihail, A., 2017. New fixed point theorems for set-valued contractions in b-metric spaces. J. Fixed Point Theory Appl, pp.1-11. Available at: https://doi.org/10.1007/s11784-016-0400-2.

Ozturk, V. & Ansari, A.H., 2017. Common fixed point theorems for mappings satisfying (E.A)-property via C-class functions in b-metric spaces. Appl. Gen. Topol., 18(1), pp.45-52. Available at: https://doi.org/10.4995/agt.2017.4573.

Parvaneh, V., Roshan, J. R., Radenović, S., 2013. Existence of tripled coincidence points in ordered b-metric spaces and an application to a system of integral equations. Fixed Point Theory Appl., 2013:130. Available at: https://doi.org/10.1186/1687-1812-2013-130.

Petrusel, A., Petrucel, G., Yao, J. C., 2017. Fixed point and coincidence point theorems in b-metric spacs with applications. Appl. Anal. Discrete Math., 11(1), pp.199-215. Available at: https://doi.org/10.2298/AADM1701199P.

Piri, H. & Kumam, P., 2016. Fixed point theorems for generalized F-Suzuki-contraction mappings in complete b-metric spaces. Fixed Point Theory Appl., 2016:90. Available at: https://doi.org/10.1186/s13663-016-0577-5.

Radenović, S., An, T.V., Quan, L.T., 2017a. Some coincidence point results for T-contraction mappings on partially ordered b-metric spaces and applications to integral equations. Nonlinear Analysis: Modelling and Control, 22(4), pp.545-565. Available at: https://doi.org/10.15388/NA.2017.4.9.

Radenović, S., Došenović, T., Ozturk, V., Dolićanin, Č., 2017b. A note on the paper: ”Nonlinear integral equations with new admissibility types in b-metric spaces”. J. Fixed Point Theory Appl. Available at: https://doi.org/10.1007/s11784-017-0416-2.

Rhoades, B. E., 1977. A comparison of various definitions of contractive mappings. Transaction of the American Mathematical Society, 226, pp.257-290. Available at: https://doi.org/10.2307/1997954.

Roshan, J.R., Parvaneh, V., Altun, I., 2014a. Some coincidence point results in ordered b-metric spaces and applications in a system of integral equations. Appl. Math. Comput., 226, pp.725-737. Available at: https://doi.org/10.1016/j.amc.2013.10.043.

Roshan, J.R., Parvaneh, V., Radenović, S., Rajović, M., 2015. Some coincidence point results for generalized -weakly contractions in ordered b-metric spaces. Fixed Point Theory Appl., 2015: 68. Available at: https://doi.org/10.1186/s13663-015-0313-6.

Roshan, J.R., Parvaneh, V., Shobkolaei, N., Sedghi, S., Shatanawi, W., 2013. Common fixed points of almost generalized ( , ) contractive mappings in ordered b-metric spaces. Fixed Point Theory Appl., 2013:159. Available at: https://doi.org/10.1186/1687-1812-2013-159.

Roshan, J.R., Shobkolaei, N., Sedghi, S., Abbas, M., 2014b. Common fixed point of four maps in b-metric spaces. Hacett. J. Math. Stat., 43(4), pp.613-624.

Sarwar, M., Jamal, N., Li, Y., 2017. Coincidence point results via generalized weak contractions in partial b-metric spaces with application. J. Nonlinear Sci. Appl., 10(7), pp.3719-3731. Available at: http://dx.doi.org/10.22436/jnsa.010.07.29.

Sarwar, M. & Rahman, M.U., 2015. Fixed point theorems for Ciric’s and generalized contractions in b-metric spaces. Int. J. Anal. Appl., 7(1), pp.70-78.

Sintunavarat, W., 2016. Nonlinear integral equations with new admissibility types in b-metric spaces. J. Fixed Point Theory Appl., 18(2), pp.397-416. Available at: https://doi.org/10.1007/s11784-015-0276-6.

Zabihi, F. & Razani, A., 2014. Fixed point theorems for hybrid rational Geraghty contractive mappings in ordered b-metric spaces. J. Appl. Math., Vol.2014, Article ID 929821. Available at: http://dx.doi.org/10.1155/2014/929821.

Zhang, C., Li, S., Liu, B., 2017. Topological structures and the coincidence point of two mappings in cone b-metric spaces. J. Nonlinear Sci. Appl., 10(4), pp.1334-1344. Available at: http://dx.doi.org/10.22436/jnsa.010.04.05.

Objavljeno
2017/10/02
Rubrika
Originalni naučni radovi