Fixed point results for \((\beta ,\alpha )\)-implicit contractions in two generalized b-metric spaces

Volume 14, Issue 1, pp 39--47 http://dx.doi.org/10.22436/jnsa.014.01.05

Publication Date: June 13, 2020 Submission Date: November 03, 2019 Revision Date: April 30, 2019 Accteptance Date: May 11, 2020

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1409 Downloads
• 2806 Views

Authors

Gehad M. Abd-Elhamed - Department of Mathematics, College of Girls, Ain Shams University, Egypt. - College of Science and Humanities studies, Sattam Bin Abdul-Aziz University, Saudi Arabia.

Abstract

The aim of this paper is to introduce (\(\beta \),\(\alpha )\)-implicit contractive of two mappings on two generalized b-metric spaces and derive some new fixed point theorems for (\(\beta \),\(\alpha )\)-implicit contractive in two complete and compact generalized b-Metric spaces.

Share and Cite

Keywords

• Fixed points
• (\(\beta \),\(\alpha )\)-implicit contractions
• generalized b-metric spaces

MSC

•  47H10
•  54H25

References

• [1] M. Abbas, B. E. Rhoades, Common fixed point results for non-commuting mappings without continuity in generalized metric spaces, Appl. Math. Comput., 215 (2009), 262--269
  • View Article
  • Google Scholar


• [2] G. M. Abd-Elhamed, Fixed point theorems for contractions and generalized contractions in $G$-metric spaces, J. Interpolat. Approx. Sci. Comput., 2015 (2015), 20--27
  • View Article
  • MathSciNet
  • Google Scholar


• [3] G. M. Abd-Elhamed, Related fixed point theorems on two complete and compact G-metric spaces, Int. J. Eng. Res. Tech., 12 (2019), 446--456
  • View Article
  • Google Scholar


• [4] R. P. Agarwal, Z. Kadelburg, S. Radenović, On coupled fixed point results in asymmetric $G$-metric spaces, J. Inequal. Appl., 2013 (2013), 12 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] A. Aghajani, M. Abbas, J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered $G_{b}$-metric spaces, Filomat, 28 (2014), 1087--1101
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [6] A. Amini-Harandi, Fixed point theory for quasi-contraction maps in $b$-metric spaces, Fixed Point Theory, 15 (2014), 351--358
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] H. Aydi, W. Shatanawi, C. Vetro, On generalized weakly $g$-contraction mapping in $g$-metric spaces, Comput. Math. Appl., 62 (2011), 4222--4229
  • View Article
  • Google Scholar
  • MATH


• [8] S. Czerwik, Nonlinear set-valued contraction mappings in $b$-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), 263--276
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] N. Hussain, C. Vetro, F. Vetro, Fixed point results for $\alpha$-implicit contractions with application to integral equations, Nonlinear Anal. Model. Control, 21 (2016), 362--378
  • View Article
  • MathSciNet
  • Google Scholar


• [10] Z. Mustafa, V. Parvaneh, M. Abbas, J. R. Roshan, Some coincidence point results for generalized $(\psi, \phi)$-weakly contractive mappings in ordered $G$-metric spaces, Fixed Point Theory Appl., 2013 (2013), 23 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [11] Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289--297
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [12] H. K. Nashine, Z. Kadelburg, Cyclic generalized $\phi$-contractions in $b$-metric spaces and an application to integral equations, Filomat, 28 (2014), 2047--2057
  • View Article
  • Google Scholar
  • MATH


• [13] V. Popa, Fixed point theorems for implicit contractive mappings, Stud. Cercet. Stiint. Ser. Mat. Univ. Bacau, 7 (1997), 129--133
  • MathSciNet
  • Google Scholar
  • MATH


• [14] V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math., 32 (1999), 157--163
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [15] V. Popa, A.-M. Patriciu, A general fixed point theorem for mappings satisfying an implicit relation in complete $G$-metric spaces, Gazi Univ. J. Sci., 25 (2012), 403--408
  • View Article
  • Google Scholar


• [16] V. Popa, A.-M. Patriciu, A general fixed point theorem for pairs of weakly compatible mappings in $G$-metric spaces, J. Nonlinear Sci. Appl., 5 (2012), 151--160
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [17] V. Popa, A.-M. Patriciu, Two general fixed point theorems for pairs of weakly compatible mappings in $G$-metric spaces, Novi Sad J. Math., 42 (2012), 49--60
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [18] V. Popa, A.-M. Patriciu, Fixed point theorems for mappings satisfying an implicit relation in complete $G$-metric spaces, Bul. Inst. Politeh. Iasi, Sect. I, Mat. Mec. Teor. Fiz., 59 (2013), 97--123
  • Google Scholar
  • MATH


• [19] S. Radenović, T. Došenović, T. A. Lampert, Z. Golubovíć, A note on some recent fixed point results for cyclic contractions in $b$-metric spaces and an application to integral equations, Appl. Math. Comput., 273 (2016), 155--164
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH