Generalized Suzuki type \( \alpha \)-\( \mathcal{Z} \)-contraction in b-metric space

Volume 13, Issue 4, pp 212--222 http://dx.doi.org/10.22436/jnsa.013.04.06

Publication Date: March 02, 2020 Submission Date: August 23, 2019 Revision Date: January 11, 2020 Accteptance Date: January 16, 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)

• 1377 Downloads
• 2401 Views

Authors

Swati Antal - Department of Mathematics, H.N.B. Garhwal University, BGR Campus, Pauri Garhwal-246001, Uttarakhand, India. U. C. Gairola - Department of Mathematics, H.N.B. Garhwal University, BGR Campus, Pauri Garhwal-246001, Uttarakhand, India.

Abstract

In this paper, we introduce the concept of generalized Suzuki type \(\alpha\)-\( \mathcal{Z} \)-contraction concerning a simulation function \(\zeta\) in b-metric space and prove the existence of fixed point results for this contraction. Our result extend the fixed point result of [A. Padcharoen, P. Kumam, P. Saipara, P. Chaipunya, Kragujevac J. Math., \(\bf 42\) (2018), 419--430].

Share and Cite

Keywords

• Simulation function
• triangular \(\alpha\)-admissible mapping with respect to \(\zeta\) \sep b-metric space
• generalized Suzuki type \(\alpha\)-\( \mathcal{Z} \)-contraction mapping

MSC

•  54H25
•  47H10

References

• [1] H. Aydi, M. Jellali, E. Karapinar, On fixed point results for $\alpha$-implicit contractions in quasi-metric spaces and consequences, Nonlinear Anal. Model. Control, 21 (2016), 40--56
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] G. V. R. Babu, D. T. Mosissa, Fixed point in $b$-metric space via simulation function, Novi Sad J. Math., 47 (2017), 133--147
  • View Article
  • MathSciNet
  • Google Scholar


• [3] M. Boriceanu, Strict fixed point theorems for multivalued operators in $b$-metric space, Int. J. Mod. Math., 4 (2009), 285--301
  • MathSciNet
  • Google Scholar


• [4] S. Czerwik, Contraction mappings in $b$-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5--11
  • View Article
  • MathSciNet
  • Google Scholar


• [5] 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


• [6] M. Demma, R. Saadati, P. Vetro, Fixed point results on $b$-metric space via Picard sequences and $b$-simulation functions, Iran. J. Math. Sci. Inform., 11 (2016), 123--136
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] E. Karapinar, P. Kumam, P. Salimi, On $\alpha$-$\psi$-Meir-Keeler contractive mappings, Fixed Point Theory Appl., 2013 (2013), 12 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] F. Khojasteh, S. Shukla, S. Radenović, A new approach to the study of fixed point theory for simulation functions, Filomat, 29 (2015), 1189--1194
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] P. Kumam, D. Gopal, L. Budhia, A new fixed point theorem under Suzuki type $Z$-contraction mappings, J. Math. Anal., 8 (2017), 113--119
  • View Article
  • MathSciNet
  • Google Scholar


• [10] B. Mohammadi, S. Rezapour, N. Shahzad, Some results on fixed points of $\alpha$-$\psi$-Ciric generalized multifunctions, Fixed Point Theory Appl., 2013 (2013), 10 pages
  • View Article
  • MathSciNet
  • Google Scholar


• [11] M. Pacurar, Sequences of almost contractions and fixed points in $b$-metric spaces, An. Univ. Vest Timiş. Ser. Mat.-Inform., 48 (2010), 125--137
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [12] A. Padcharoen, P. Kumam, P. Saipara, P. Chaipunya, Generalized Suzuki type $\mathcal{Z}$-contraction in complete metric spaces, Kragujevac J. Math., 42 (2018), 419--430
  • View Article
  • Google Scholar


• [13] J. R. Roshan, V. Parvaneh, Z. Kadelberg, Common fixed point theorems for weakly isotone increasing mappings in ordered $b$-metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 229--245
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [14] J. R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei, W. Shatanawi, Common fixed points of almost generalized $(\psi, \phi){s}$-contractive mappings in ordered $b$-metric spaces, Fixed Point Theory Appl., 2013 (2013), 23 pages
  • View Article
  • MathSciNet
  • Google Scholar


• [15] B. Samet, C. Vetro, P. Vetro, Fixed point theorem for $\alpha-\psi$-contractive type mappings, Nonlinear Anal., 75 (2012), 2154--2165
  • View Article
  • MathSciNet
  • Google Scholar