Fisher type fixed point results in controlled metric spaces

Volume 20, Issue 3, pp 234--240 http://dx.doi.org/10.22436/jmcs.020.03.06

Publication Date: February 05, 2020 Submission Date: September 14, 2019 Revision Date: November 11, 2019 Accteptance Date: November 27, 2019

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Authors

Durdana Lateef - Department of Mathematics, College of Science, Taibah University, Madina, 41411, Saudi Arabia.

Abstract

In the present paper, we define a rational contractive condition of Fisher type in the context of controlled metric space and obtain some generalized fixed point results in this space. These results will unify and amend many well-known results of literature. Some consequences and an example has been presented at the end to show the authenticity of the established results.

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Keywords

• Fixed point
• rational contraction
• controlled metric spaces

MSC

•  47H10
•  54H25
•  65Q10

References

• [1] T. Abdeljawad, N. Mlaiki, H. Aydi, N. Souayah, Double Controlled Metric Type Spaces and Some Fixed Point Results, Mathematics, 6 (2018), 10 pages
  • View Article
  • Google Scholar
  • MATH


• [2] J. Ahmad, A. E. Al-Mazrooei, Y. J. Cho, Y.-O. Yang, Fixed point results for generalized $\Theta $-contractions, J. Nonlinear Sci. Appl., 10 (2017), 2350--2358
  • View Article
  • MathSciNet
  • Google Scholar


• [3] J. Ahmad, A. S. Al-Rawashdeh, A. Azam, Fixed point results for $\{\alpha, \xi \}$-expansive locally contractive mappings, J. Inequal. Appl., 2014 (2014), 10 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] J. Ahmad, A. Al-Rawashdeh, A. Azam, New fixed point theorems for generalized $F$-contractions in complete metric spaces, Fixed Point Theory Appl., 2015 (2015), 18 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] L. A. Alnaser, D. Lateef, H. A. Fouad, J. Ahmad, Relation theoretic contraction results in $\mathcal{F}$-metric spaces, J. Nonlinear Sci. Appl., 12 (2019), 337--344
  • View Article
  • MathSciNet
  • Google Scholar


• [6] B. Alqahtani, E. Karapinar, A. Öztürk, On ($\alpha-\psi$)-$K$-contractions in the extended $b$-metric space, Filomat, 32 (2018), 5337--5345
  • View Article
  • MathSciNet
  • Google Scholar


• [7] Z. Aslam, J. Ahmad, N. Sultana, New common fixed point theorems for cyclic compatible contractions, J. Math. Anal., 8 (2017), 1--12
  • View Article
  • MathSciNet
  • Google Scholar


• [8] A. Azam, N. Mehmood, J. Ahmad, S. Radenović, Multivalued fixed point theorems in cone $b$-metric spaces, J. Inequal. Appl., 2013 (2013), 9 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] S. Banach, Stefan Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133--181
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


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


• [11] B. Fisher, Mappings satisfying a rational inequality, Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.), 24 (1980), 247--251
  • View Article
  • MathSciNet
  • Google Scholar


• [12] H. P. Huang, S. Radenović, Some fixed point results of generalised Lipschitz mappings on cone b-metric spaces over Banach algebras, J. Comput. Anal. Appl., 20 (2016), 566--583
  • View Article
  • Google Scholar


• [13] N. Hussain, J. Ahmad, A. Azam, On Suzuki--Wardowski type fixed point theorems, J. Nonlinear Sci. Appl., 8 (2015), 1095--1111
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [14] N. Hussain, A. E. Al-Mazrooei, J. Ahmad, Fixed point results for generalized ($\alpha $-$\eta $)--$\Theta $ contractions with applications, J. Nonlinear Sci. Appl., 10 (2017), 4197--4208
  • View Article
  • MathSciNet
  • Google Scholar


• [15] 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


• [16] T. Kamran, M. Samreen, Q. UL Ain, A generalization of $b$-metric space and some fixed point theorems, Mathematics, 5 (2017), 7 pages
  • View Article
  • Google Scholar
  • MATH


• [17] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 60 (1968), 71--76
  • View Article


• [18] E. Karapınar, P. Kumari, D. Lateef, A New Approach to the Solution of the Fredholm Integral Equation via a Fixed Point on Extended $b$-Metric Spaces, Symmetry, 10 (2018), 13 pages
  • View Article
  • Google Scholar


• [19] M. A. Kutbi, J. Ahmad, A. Azam, On fixed points of $\alpha$-$\psi$-contractive multi-valued mappings in cone metric spaces, Abst. Appl. Anal., 2013 (2013), 13 pages
  • Google Scholar


• [20] D. Lateef, J. Ahmad, Dass and Gupta's fixed point theorem in $F$-metric spaces, J. Nonlinear Sci. Appl., 12 (2019), 405--411
  • View Article
  • MathSciNet
  • Google Scholar


• [21] N. Mlaiki, H. Aydi, N. Souayah, T. Abdeljawad, Controlled Metric Type Spaces and the Related Contraction Principle, Mathematics, 6 (2018), 7 pages
  • View Article
  • Google Scholar


• [22] W. Onsod, T. Saleewong, J. Ahmad, A. E. Al-Mazrooei, P. Kumam, Fixed points of a $\Theta$--contraction on metric spaces with a graph, Commun. Nonlinear Anal., 2 (2016), 139--149
  • Google Scholar


• [23] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), 6 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH