Neke teoreme o fiksnoj tački u b2-metričkim prostorima

  • Poom Kumam King Mongkuts University of Technology Thonburi, Faculty of Science, KMUTT-Fixed Point Theory and Applications Research Group Theoretical and Computational Science Center (TaCS) Science Laboratory Building
  • Zoran D. Mitrović University of Banja Luka, Faculty of Electrical Engineering
  • Mirjana V. Pavlović University of Kragujevac, Faculty of Science, Department of Mathematics and Informatics
Ključne reči: fixed points||, ||fiksne tačke, common fixed points||, ||zajedničke fiksne tačke, 2-metric space||, ||2-metrički prostor, b2-metric space||, ||b2-metrički prostor,

Sažetak


U ovom radu prvo je dokazan rezultat koji daje dovoljan uslov za konvergenciju nizova u b2-metričkom prostoru. Takođe, navedene su neke teoreme o fiksnoj tački u b2-metričkom prostoru. Neki rezultati predstavljaju odgovarajuće generalizacije poznatih rezultata u b2-metričkom prostoru, a primeri su prezentirani da to potvrde.

Reference

Agarwal, R.P., Karapınar, E., O’Regan, D., & Roldán-López-de-Hierro, A.F. 2015. Fixed Point Theory in Metric Type Spaces.Cham: Springer Nature. Available at: https://doi.org/10.1007/978-3-319-24082-4.

Ahmed, M.A. 2009. A common fixed point theorem for expansive mappings in 2-metric spaces and its application. Chaos, Solitons and Fractals, 42(5), pp.2914-2920. Available at: https://doi.org/10.1016/j.chaos.2009.04.034.

Aleksić, S., Mitrović, Z.D., & Radenović, S. 2018. A fixed point theorem of Jungck in bv(s)-metric spaces. Periodica Mathematica Hungarica, 77(2), pp.224-231. Available at: https://doi.org/10.1007/s10998-018-0236-1.

Aliouche, A., & Simpson, C. 2012. Fixed points and lines in 2-metric spaces. Advances in Mathematics, 229(1), pp.668-690. Available at: https://doi.org/10.1016/j.aim.2011.10.002.

Aydi, H. 2016. Implicit contractive pair of mappings on quasi b-metric spaces and an application to integral equations. J. Nonlinear Convex Anal, 17(12), pp.2417-2433. Available at: https://scholar.google.com/scholar?cluster=11178112980716461515&hl=en&as_sdt=2005&sciodt=0,5. Accessed:30.03.2019.

Bakhtin, I.A., 1989. The contraction mapping principle in quasimetric spaces. Func. An., Gos. Ped. Inst. Unianowsk,30, pp.26-37.

Czerwik, S. 1993. Contraction mappings in b-metric spaces. Acta Mathematica et Informatica Universitatis Ostraviensis, 1, pp.5-11. Available at: https://dml.cz/handle/10338.dmlcz/120469. Accessed:30.03.2019.

Czerwik, S. 1998. Nonlinear setvalued contraction mappings in b-metric spaces. Atti Sem. Mat. Univ. Modena, 46, pp.263-276.

Ćirić, Lj. 2003. Fixed Point Theory: Contraction Mapping Principle.Belgrade: Faculty of Mechanical Engineering.

Deshpande, B., & Chouhan, S. 2011. Common fixed point theorems for hybrid pairs of mappings with some weaker conditions in 2-metric spaces. Fasc. Math, 46, pp.37-55. Available at: http://www.math.put.poznan.pl/artykuly/FM46(2011)-DeshpandeB-ChouhanS.pdf. Accessed: 30.03.2019.

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

Dung, N.V., & Le Hang, V.T. 2013. Fixed point theorems for weak C-contractions in partially ordered 2-metric spaces. Fixed Point Theory and Applications, 2013:161. Available at: https://doi.org/10.1186/1687-1812-2013-161.

Fadail, Z.M., Ahmad, A.G.B., Ozturk, V., & Radenović, S. 2015. Some remarks on fixed point results of b2-metric spaces. Far East Journal of Mathematical Sciences (FJMS), 97(5), pp.533-548. Available at: https://doi.org/10.17654/fjmsjul2015_533_548.

Freese, R.W., Cho, J.Y., & Kim, S.S. 1992. Strictly 2-convex linear 2-normed spaces. J. Korean Math. Soc., 29(2), pp.391-400. Available at: http://pdf.medrang.co.kr/kms01/JKMS/29/JKMS-29-2-391-400.pdf. Accessed: 30.03.2019.

Gähler, S. 1963. 2-metrische Räume und ihre topologische Struktur. Mathematische Nachrichten, 26(1-4), pp.115-148 (in German). Available at: https://doi.org/10.1002/mana.19630260109.

George, R., Radenović, S., Reshma, K.P., & Shukla, S. 2015. Rectangular b-metric space and contraction principles. Journal of Nonlinear Sciences and Applications, 8(6), pp.1005-1013. Available at: https://doi.org/10.22436/jnsa.008.06.11.

Iseki, K. 1975. Fixed point theorems in 2-metric spaces. Math. Semin Notes, 3, pp.133-136.

Iseki, K. 1976. Mathematics on 2-normed spaces. Bull. Korean Math. Soc, 13(2), pp.127-135.

Jungck, G. 1976. Commuting Mappings and Fixed Points. The American Mathematical Monthly, 83(4), pp.261-263. Available at: https://doi.org/10.1080/00029890.1976.11994093.

Kannan, R. 1968. Some results on fixed points. Bull. Calcutta Math. Soc, 60, pp.71-76.

Kirk, W., & Shahzad, N. 2014. Fixed Point Theory in Distance Spaces.Cham: Springer Nature. Available at: https://doi.org/10.1007/978-3-319-10927-5.

Lahiri, B.K., Das, P., & Dey, L.K. 2011. Cantor’s Theorem in 2-Metric Spaces and its Applications to Fixed Point Problems. Taiwanese Journal of Mathematics, 15(1), pp.337-352. Available at: https://doi.org/10.11650/twjm/1500406178.

Lal, S.N., & Singh, A.K. 1978. An analogue of Banach's contraction principle for 2-metric spaces. Bulletin of the Australian Mathematical Society, 18(1), pp.137-143. Available at: https://doi.org/10.1017/s0004972700007887.

Miculescu, R., & Mihail, A. 2017. New fixed point theorems for set-valued contractions in b-metric spaces. Journal of Fixed Point Theory and Applications, 19(3), pp.2153-2163. Available at: https://doi.org/10.1007/s11784-016-0400-2.

Mitrović, Z.D., & Radenović, S. 2017. The Banach and Reich contractions in bv(s)-metric spaces. Journal of Fixed Point Theory and Applications, 19(4), pp.3087-3095. Available at: https://doi.org/10.1007/s11784-017-0469-2.

Mitrović, Z.D., & Radenović, S. 2017. A common fixed point theorem of Jungck in rectangular b-metric spaces. Acta Mathematica Hungarica, 153(2), pp.401-407. Available at: https://doi.org/10.1007/s10474-017-0750-2.

Mustafa, Z., Parvaneh, V., Roshan, J.R., & Kadelburg, Z. 2014. b2-metric spaces and some fixed point theorems. Fixed Point Theory and Applications, 2014:144. Available at: https://doi.org/10.1186/1687-1812-2014-144.

Naidu, S.V.R., & Prasad, J.R. 1986. Fixed point theorems in 2-metric spaces. Indian J. Pure Appl. Math, 17(8), pp.974-993.

Popa, V., Imdad, M., & Ali, J. 2010. Using implicit relations to prove unified fixed point theorems in metric and 2-metric spaces. Bull. Malays. Math. Sci. Soc., 33(1), pp.105-120. Available at: http://emis.ams.org/journals/BMMSS/pdf/v33n1/v33n1p8.pdf. Accessed:30.03.2019.

Reich, S. 1971. Some Remarks Concerning Contraction Mappings. Canadian Mathematical Bulletin, 14(1), pp.121-124. Available at: https://doi.org/10.4153/cmb-1971-024-9.

Objavljeno
2019/04/08
Rubrika
Originalni naučni radovi