Some Fixed Point Theorems for Generalized \(\alpha\)-\(\eta\)-\(\psi\)-Geraghty Contractive Type Mappings in Partial \(b\)-Metric Spaces

Authors

  • A. Farajzadeh Department of Mathematics, Razi University, Kermanshah, 67149
  • C. Noytaptim Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000
  • A. Kaewcharoen Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000

DOI:

https://doi.org/10.26713/jims.v10i3.583

Keywords:

Generalized \(\alpha\)-\(\eta\)-\(\psi\)-Geraghty contractive type mappings, \(\alpha\)-orbital attractive mappings with respect to \(\eta\), Complete partial \(b\)-metric spaces, Fixed points

Abstract

In this paper, we introduce the notion of generalized \(\alpha\)-\(\eta\)-\(\psi\)-Geraghty contractive type mappings in the set up of partial \(b\)-metric spaces and \(\alpha\)-orbital attractive mappings with respect to \(\eta\). Furthermore, the fixed point theorems for such mappings in complete partial \(b\)-metric spaces are proven without assuming the subadditivity of \(\psi\). Some examples are also provided for supporting of our main results.

Downloads

Download data is not yet available.

References

A. Amini-Harandi and H. Emami, A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal. 72(2010), 2238 – 2242.

I.A. Bakhtin, The contraction principle in quasimetric spaces, Funct. Anal. 30 (1989), 26 – 37.

S. Banach, Sur les operations dans les ensembles abstraits et leur applications aux equations integrales, Fundam. Math. 3 (1922), 133 – 181.

S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav. 1 (1993), 5 – 11.

S.H. Cho, J.S. Bae and E. Karapınar, Fixed point theorems for (alpha)-Geraghty contraction type maps in metric spaces, J. Inequal. Appl. 2013, 329.

P. Chuadchawna, A. Kaewcharoen and S. Plubtieng, Fixed point theorems for generalized (alpha)-(eta)-(psi)-Geraghty contraction type mappings in (alpha)-(eta)-complete metric spaces, J. Nonlinear Sci. Appl. 9 (2016), 471 – 485.

M. Geraghty, On contractive mappings, Proc. Amer Math. Soc. 40 (1973), 604 – 608.

E. Karapinar and B. Samet, Generalized (alpha)-(psi)-contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal. 2012 (2012), 17 pages.

E. Karapinar, P. Kumam and P. Salimi, On (alpha)-(psi)-Meir-Keeler contractive mappings, J. Inequal. Appl. 94 (2013).

E. Karapinar, (alpha)-(psi)-Geraghty contraction type mappings and some related fixed point results, Filomat 28(1) (2014), 37 – 48.

M.S. Khan, M. Swaeh and S. Sessa, Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc. 30 (1984), 1 – 9.

P. Kumam, N.V. Dung and V.T.L. Hang, Some equivalences between cone b-metric spaces and b-metric spaces, Abstr. Appl. Anal. 2013 (2013), 8 pages.

S.G. Matthews, Partial metric topology, Proc. 8th Summer Conference on General Topology and Applications, Ann. N.Y. Acad. Sci. 728 (1994), 183 – 197.

A. Mukheimer, (alpha)-(psi)-(varphi)-contractive mappings in ordered partial b-metric spaces, J. Nonlinear Sci. Appl. 7 (2014), 168 – 179.

Z. Mustafa, J. Rezaei Roshan, V. Parvaneh and Z. Kadelburg, Some common fixed point results in ordered partial b-metric spaces, J. Inequal. Appl. 2013 (2013), 526.

O. Popescu, Some new fixed point theorems for (alpha)-Geraghty contraction type maps in metric spaces, J. Inequal. Appl. 2014 (2014), 190.

V.L. Rosa and P. Vetro, Fixed points for Geraghty-contractions in partial metric spaces, J. Nonlinear Sci. Appl. 7 (2014), 1 – 10.

P. Salimi, A. Latif and N. Hussain, Modified (alpha)-(psi)-contractive mappings with applications, Fixed Point Theory Appl. 2013 (2013), 151.

B. Samet, C. Vetro and P. Vetro, Fixed point theorems for (alpha)-(psi)-contractive type mappings, Nonlinear Anal. 75 (2012), 2154 – 2165.

K.P.R. Sastry, K.K.M. Sarma, Ch. Srinivasa Rao and V. Perraju, Fixed point theorems for Geraghty contractions in partially ordered partial b-metric spaces, Func. Anal. - TMA 1 (2015), 8 – 19.

S. Shukla, Partial b-metric spaces and fixed point theorems, Mediterr. J. Math. 11 (2014), 703 – 711.

Downloads

Published

2018-09-30
CITATION

How to Cite

Farajzadeh, A., Noytaptim, C., & Kaewcharoen, A. (2018). Some Fixed Point Theorems for Generalized \(\alpha\)-\(\eta\)-\(\psi\)-Geraghty Contractive Type Mappings in Partial \(b\)-Metric Spaces. Journal of Informatics and Mathematical Sciences, 10(3), 455–578. https://doi.org/10.26713/jims.v10i3.583

Issue

Vol. 10 No. 3 (2018)

Section

Research Articles

License

Authors who publish with this journal agree to the following terms:
  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.