Theoretical fixed point theorem on S-metric space under binary relation via implicit contractive condition with an application
Downloads
Abstract
In this paper, we extend and generalises the results by Ahmadullah et al. to self mappings on the S-metric space under a binary relation via implicit contractive condition with an application to an integral equation. We also provided an illustrative example.
Keywords:
S-metric space, binary relation, self-mapping, fixed point, implicit relation, integral equationMathematics Subject Classification:
Mathematics- Pages: 1019-1028
- Date Published: 01-01-2021
- Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
Alam, A., Imdad, M.: Relation-theoretic metrical coincidence theorems. Filomat, 31(14) (2017), 4421-4439.
Ahmadullah, M. D., Javid, A., Imdad, M.: Unified relation-theoretic metrical fixed point theorems under an implicit contractive condition with an application. Füed Point Theory and Application, 2016(1) (2016), 1-15.
Ahmadullah, M. D., Khan, A. R., Imdad, M.: Relationtheoretic contraction principle in metric-like as well as partial metric spaces. Bull. Math. Anal. Appl., 9(3) (2017), $31-41$.
Alam, A., Imdad, M.: Relation-theoretic contraction principle. J. Fixed Point Theory Appl., 17 (4) (2015), 693702.
Dhage, B. C.: Generalised metric space and topological structure. I. Analele Atintifice ale Universitatii Al. I. Cuza din lasi. Serie Noua Mathematica, 46(3) (2000), 1-24.
Chaipornjareansri, S.: Fixed point theorems for generalised weakly contractive mappings in S-metric spaces. Thai Journal of mathematics, (2018) (2018), 50-62.
Gubran. R., Imdad, M., Ahmadullah, M. D.: Relationtheoretic metrical fixed point theorems under nonlinear contractions. Fixed Point Theory, 2016 (2016), 1-18.
Imdad, M., Kumar Santosh and Khan M. S.,Remarks on some fixed point theorems satisfying implicit relations, Radovi Matematicki, 11(1) (2002), 135-143.
Kim, J. K., Sedghi, S., Gholidahneh, A., Rezaee, M. M.: Fixed point theorems in S-metric spaces. East Asian Math. J., 32(5) (2016), 677-684.
Kolman, B., Busby,R. C., Ross, S.: Discrete mathematical structures. 3rd edn. PHI Pvt. Ltd, New Delhi (2000).
Lipschutz, S.: Schaum's Outlines of Theory and Problems of Set Theory and Related Topics. McGraw-Hill, New York (1964).
Maddux, R. D.: Relation Algebras. Studies in Logic and the Foundations of Mathematics, Elsevier, Amsterdam, $150(2006)$.
Özgür, N. Y., Taş, N.: The Picard theorem on S-metric spaces. Acta Mathematica Scientia., 38(4) (2018), 12451258
Popa, V., Patriciu, A.: Fixed point for compatible mappings in S-metric spaces. Scientific Studies and Research. Series Mathematics and Informatics, 28(2) (2018), 6378.
Samet, B., Turinici, M.: Fixed point theorems on a metric space endowed with an arbitrary binary relation and applications. Commun. Math. Anal., 13 (2012), 82-97.
Sedghi, S., Van Dung, N.: Fixed point theorems on Smetric spaces. Matematički Vesnik, 255 (2014), 113-124.
Sedghi, S., Shobe, N., Aliouche, A.: A generalisation of fixed point theorem in S-metric spaces. Matematicki Vesnik, 64 (2012), 258-266.
Sedghi, S., Shobkolaei, N., Shahraki, M., Došenović, T.: Common fixed point for four maps in $S$ - metric spaces. Mathematical Sciences, 12 (2) (2018), 137-143.
Roldan Lopez de Hierro, A. F.: A unified version of Ran and Reurings theorem and Nieto and RodriguezLopezs theorem and low-dimensional generalisations. Appl. Math. Inf. Sci., 10 (2016), 383-393.
Similar Articles
- A. Vijayalekshmi, S. Abisha, An introduction of total dominator color class total dominating sets in graphs , Malaya Journal of Matematik: Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
- A. Vijayalekshmi, A. E. Prabha, Introduction of color class dominating sets in graphs , Malaya Journal of Matematik: Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)
- A. Vijayalekshmi, S. Abisha, Total dominator color class total dominating sets in Dutch windmill graph and coconut tree graph , Malaya Journal of Matematik: Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
- A. Vijayalekshmi, P. Niju, Dominator color class dominating sets on fire cracker, gear and flower graphs , Malaya Journal of Matematik: Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
- A. E. Prabha, A. Vijayalekshmi, Color class dominating sets in ladder and grid graphs , Malaya Journal of Matematik: Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
- A. Vijayalekshmi, S. Abisha, Total dominator color class total dominating sets in ladder and mobius ladder graph , Malaya Journal of Matematik: Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
- A. Vijayalekshmi, A. E. Prabha, Color class dominations sets in various classes of graphs , Malaya Journal of Matematik: Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
- S. K. Vaidya, A. D. Parmar, On chromatic transversal domination in graphs , Malaya Journal of Matematik: Vol. 7 No. 03 (2019): Malaya Journal of Matematik (MJM)
- B. Chaluvaraju, C. Appajigowda, The dom-chromatic number of a graph , Malaya Journal of Matematik: Vol. 4 No. 01 (2016): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.