New fixed point results in bv(s)-metric spaces
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Tatjana Došenović
,
Zoran Kadelburg
Abstract
Z. D. Mitrović and S. Radenović introduced in [The Banach and Reich contractions inbv(s)-metric spaces, J. Fixed Point Theory Appl. 19 (2017), 3087–3095] a new class of generalized metric spaces and proved some fixed point theorems in this framework. The purpose of this paper is to consider other kinds of contractive mappings in bv(s)-metric spaces, and show how the work in the new settings differs from the one in standard metric and b-metric spaces. Examples show the usefulness of the obtained results.
We wish to thank the projects MNTRRS-174009 and Ministry for Scientific and Technological Development, Higher Education and Information Society of Republika Srpska (Savremena istraživanja u teoriji fiksne tačke: metrički i topološki pristup, 1255007.)
(Communicated by Gregor Dolinar )
References
[1] Abbas, M.—Chema, I. Z.—Razani, A.: Existence of common fixed point for b-metric rational type contraction, Filomat 30(6) (2016), 1413–1429.10.2298/FIL1606413ASuche in Google Scholar
[2] Aleksić, S.—Mitrović, Z.D.—Radenović, S.: A fixed point theorem of Jungck inbv(s)-metric spaces, Period. Math. Hungar., to appear, https://doi.org/10.1007/s10998-018-0236-1.10.1007/s10998-018-0236-1Suche in Google Scholar
[3] Bakhtin, I. A.: The contraction mapping principle in quasimetric spaces, Funct. Anal. 30 (1989), 26–37.Suche in Google Scholar
[4] Berinde, V.: Approximation fixed points of weak contractions using Picard iteration, Nonlinear Anal. Forum 9(1) (2004), 43–53.10.1155/S1687182004311058Suche in Google Scholar
[5] Branciari, A.: A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen 57 (2000), 31–37.10.5486/PMD.2000.2133Suche in Google Scholar
[6] Czerwik, S.: Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav. 1 (1993), 5–11.Suche in Google Scholar
[7] Garai, H.: Personal communication.Suche in Google Scholar
[8] George, R.—Radenović, S.—Reshma, K. P.—Shukla, S.: Rectangular b-metric space and contraction principles, J. Nonlinear Sci. Appl. 8 (2015), 1005–1013.10.22436/jnsa.008.06.11Suche in Google Scholar
[9] Geraghty, M.: On contractive mappings, Proc. Amer. Math. Soc. 40 (1973), 604–608.10.1090/S0002-9939-1973-0334176-5Suche in Google Scholar
[10] Hussain, N.—Parvaneh, V.—Roshan, J.R.—Kadelburg, Z.: Fixed points of cyclic (ψ, φ, L, A, B)-contractive mappings in orderedb-metric spaces with applications, Fixed Point Theory Appl. 2013(256) (2013), 1–18.10.1186/1687-1812-2013-256Suche in Google Scholar
[11] Jovanović, M.—Kadelburg, Z.—Radenović, S.: Common fixed point results in metric type spaces, Fixed Point Theory Appl. 2010 (2010), Art. ID 978121.10.1155/2010/978121Suche in Google Scholar
[12] Kadelburg, Z.—Radenović, S.: On generalized metric spaces: a survey, TWMS J. Pure Appl. Math. 5(1) (2014), 3–13.Suche in Google Scholar
[13] Kumam, P.—Rouzkard, F.—Imdad, M.—Gopal, D.: Fixed point theorems on ordered metric spaces through a rational contraction, Abstr. Appl. Anal. 2013 (2013), Art. ID 206515.10.1155/2013/206515Suche in Google Scholar
[14] Miculescu, R.—Mihail, A.: New fixed point theorems for set-valued contractions in b-metric spaces, J. Fixed Point Theory Appl. 19(3) (2017), 2153–2163.10.1007/s11784-016-0400-2Suche in Google Scholar
[15] Mitrović, Z. D.—Radenović, S.: The Banach and Reich contractions inbv(s)-metric spaces, J. Fixed Point Theory Appl. 19 (2017), 3087–3095.10.1007/s11784-017-0469-2Suche in Google Scholar
[16] Roshan, J. R.—Parvaneh, V.—Kadelburg, Z.—Hussain, N.: New fixed point results inb-rectangular metric spaces, Nonlinear Anal. Model. Control. 21(5) (2016), 614–634.10.15388/NA.2016.5.4Suche in Google Scholar
[17] Singh, S. L.—Czerwik, S.—Krol, K.—Singh, A.: Coincidences and fixed points of hybrid contractions, Tamsui Oxf. J. Math. Sci. 24 (2008), 401–416.Suche in Google Scholar
[18] Suzuki, T.—Alamri, B.—Kikkawa, M.: Only 3-generalized metric spaces have a compatible symmetric topology, Open Math. 13 (2015), 510–517.10.1515/math-2015-0048Suche in Google Scholar
[19] Zheng, D.—Wang, P.—Čitaković, N.: Meir-Keeler theorem in b-rectangular metric spaces, J. Nonlinear Sci. Appl. 10(4) (2017), 1786–1790.10.22436/jnsa.010.04.39Suche in Google Scholar
© 2020 Mathematical Institute Slovak Academy of Sciences
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- New fixed point results in bv(s)-metric spaces
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Artikel in diesem Heft
- Regular papers
- Relatively residuated lattices and posets
- Strongly s-dense injective hull and Banaschewski’s theorems for acts
- Wild sets in global function fields
- Generators and integral points on elliptic curves associated with simplest quartic fields
- New Filbert and Lilbert matrices with asymmetric entries
- Returning functions with closed graph are continuous
- On sets of points of approximate continuity and ϱ-upper continuity
- Investigation of the fifth Hankel determinant for a family of functions with bounded turnings
- On solvability of some nonlocal boundary value problems for biharmonic equation
- The study of piecewise pseudo almost periodic solutions for impulsive Lasota-Wazewska model with discontinuous coefficients
- Strongly increasing solutions of higher-order quasilinear ordinary differential equations
- Oscillation of second order half-linear neutral differential equations with weaker restrictions on shifted arguments
- Filippov solutions of vector Dirichlet problems
- Sequences of positive homoclinic solutions to difference equations with variable exponent
- Modified Lupaş-Jain operators
- New fixed point results in bv(s)-metric spaces
- Improved Young and Heinz operator inequalities for unitarily invariant norms
- Scrutiny of some fixed point results by S-operators without triangular inequality
- The lattices of families of regular sets in topological spaces
- Iterated partial summations applied to finite-support discrete distributions
- Hamiltonicity of a class of toroidal graphs
