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Common fixed point theorems for a class of (s, q)-contractive mappings in b-metric-like spaces and applications to integral equations

  • Kastriot Zoto EMAIL logo , Billy E. Rhoades and Stojan Radenović
Published/Copyright: January 22, 2019
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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.

  1. (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

Received: 2017-05-23
Accepted: 2018-04-08
Published Online: 2019-01-22
Published in Print: 2019-02-25

© 2019 Mathematical Institute Slovak Academy of Sciences

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