Abstract
In this paper, we establish fixed point theorems for one and two selfmaps in b-metric-like spaces, using (s, q)-contractive and F-(ψ, φ, s, q)-contractive conditions, defined by means of altering distances and 𝓒-class functions. Our theorems unify, extend and generalize corresponding results in the literature.
(Communicated by Gregor Dolinar)
References
[1] Alghmandi, M. A.—Hussain, N.—Salimi, P.: Fixed point and coupled fixed point theorems on b-metric-like spaces, J. Inequal. Appl. 2013 (2013), Art. 402.10.1186/1029-242X-2013-402Search in Google Scholar
[2] Amini-Harandi, A.: Metric-like spaces, partial metric spaces and fixed points, J. Fixed Point Theory Appl. 2012 (2012), Art. 204.10.1186/1687-1812-2012-204Search in Google Scholar
[3] Ansari, A. H.: Note on (ψ, φ)-contractive type mappings and related fixed point. The second Regional Conference on Mathematics And Applications, Payame Noor University, September 2014, pp. 377–380.Search in Google Scholar
[4] Ansari, A. H.—Chandok, S.—Ionescu, C.: Fixed point theorems on b-metric spaces for weak contractions with auxiliary functions, J. Inequal. Appl. 2014 (2014).10.1186/1029-242X-2014-429Search in Google Scholar
[5] Arshad, M.—Karapinar, E.—Ahmad, J.: Some unique fixed point theorems for rational contractions in partially ordered metric spaces, J. Inequal. Appl. 2013 (2013), Art. 248.10.1186/1029-242X-2013-248Search in Google Scholar
[6] Aydi, H.—Karapinar E.: Fixed point results for generalized α-ψ -contractions in metric-like spaces and applications, Electron. J. Differential Equations 133 (2015), 1–15.Search in Google Scholar
[7] Bakhtin, I. A.: The contraction mapping principle in quasimetric spaces, Funct. Anal., Unianowsk Gos. Ped. Inst. 30 (1989), 26–37.Search in Google Scholar
[8] Chen, C.—Dong, J.—Zhu, C.: Some fixed point theorems in b-metric-like spaces, J. Fixed Point Theory Appl. 122 (2015).10.1186/s13663-015-0369-3Search in Google Scholar
[9] Czerwik, S. Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav. 1(1) (1993), 5–11.Search in Google Scholar
[10] Dass, B. K.—Gupta, S: An extension of Banach contraction principle through rational expressions, Indian J. Pure Appl. Math. 6 (1975), 1455–1458.Search in Google Scholar
[11] Doric, D.: Common fixed point for generalized (ψ, φ)-weak contractions, Appl. Math. Lett. 22 (2009), 1896–1900.10.1016/j.aml.2009.08.001Search in Google Scholar
[12] Fadail, Z. M.—Ghafur Bin Ahmad, A.—Ansari, A. H.—Radenović, S.—Rajović, M.: Some common fixed point results of mappings in 0-complete metric-like spaces via new function, Appl. Math. Sci. 9 (2015).10.12988/ams.2015.53192Search in Google Scholar
[13] Hitzler, P.—Seda, A. K.: Dislocated topologies, J. Electr. Engin. 51(12/S):3:7 (2000).Search in Google Scholar
[14] Hoxha, E.—Ansari, A. H.—Zoto K. Some common fixed point results through generalized altering distances on dislocated metric spaces, Proceedings of EIIC, September 1–5, (2014), 403–409.Search in Google Scholar
[15] Hussain, N.—Roshan, J. R.—Parvaneh, V.—Abbas, M.: Common fixed point results for weak contractive mappings in ordered b-dislocated metric spaces with applications, J. Inequal. Appl. 2013 (2013), Art. 486.10.1186/1029-242X-2013-486Search in Google Scholar
[16] Hussain, N.—Roshan, J. R.—Parvaneh, V.—Kadelburg, Z.: Fixed points of contractive mappings in b-metric-like spaces, The Scientific World Journal 2014 (2014), Art. 471827.10.1155/2014/471827Search in Google Scholar PubMed PubMed Central
[17] Jaggi, D. S.: Some unique fixed point theorems, Indian J. Pure Appl. Math. 8 (1977), 223–230.Search in Google Scholar
[18] Karapinar, E.—Salimi P.: Dislocated metric space to metric spaces with some fixed point theorems, J. Fixed Point Theory Appl. 2013 (2013), Art. 222.10.1186/1687-1812-2013-222Search in Google Scholar
[19] Kumar, M. P.—Sachdeva, S.—Banerjee, S. K.: Some fixed point theorems in b-metric space, Turkish Journal of Analysis and Number Theory 2(1) (2014), 19–22.10.12691/tjant-2-1-5Search in Google Scholar
[20] Mustafa, Z.—Roshan, J. R.—Parvaneh, V.—Kadelburg, Z.: Some common fixed point results in ordered partial b-metric spaces, J. Inequal. Appl. 2013 (2013), Art. 562.10.1186/1029-242X-2013-562Search in Google Scholar
[21] Rhoades, B. E.: Some theorems on weakly contractive maps. Nonlinear Anal. 47(4) (2001), 2683–2693.10.1016/S0362-546X(01)00388-1Search in Google Scholar
[22] Salimi, P.—Hussain, N.—Shukla, S.—Fathollahi, Sh.—Radenović, S.: Fixed point results for cyclic α-ψ-φ-contractions with application to integral equations, J. Comput. Appl. Math. 290 (2015), 445–458.10.1016/j.cam.2015.05.017Search in Google Scholar
© 2019 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Prof. RNDr. pavel brunovský, DrSc. passed away ∗dec. 5, 1934 – † dec. 14, 2018
- Ideals and congruences in pseudo-BCH algebras
- Regular double p-algebras
- Distributive nearlattices with a necessity modal operator
- States in generalized probabilistic models: An approach based in algebraic geometry
- Free power-associative n-ary groupoids
- On the 2-class field tower of subfields of some cyclotomic ℤ2-extensions
- On the space of generalized theta-series for certain quadratic forms in any number of variables
- Uniqueness and periodicity for meromorphic functions with partial sharing values
- Mild solution of stochastic partial differential equation with nonlocal conditions and noncompact semigroups
- An inverse boundary problem for fourth-order Schrödinger equations with partial data
- Entropy as an integral operator
- Global behavior of two third order rational difference equations with quadratic terms
- Measures on effect algebras
- Some topological and combinatorial properties preserved by inverse limits
- The convergence-theoretic approach to weakly first countable spaces and symmetrizable spaces
- Compositions of porouscontinuous functions
- A note on prime divisors of polynomials P(Tk); k ≥ 1
- On complete convergence for weighted sums of arrays of rowwise END random variables and its statistical applications
- Common fixed point theorems for a class of (s, q)-contractive mappings in b-metric-like spaces and applications to integral equations