Research Article

COMMON COUPLED FIXED POINT THEOREMS FOR GENERALIZED NONLINEAR CONTRACTIONS ON METRIC SPACES INVOLVING A GRAPH

Volume: 36 Number: 2 June 1, 2018
  • Esra Yolaçan
  • Pradip Debnath
  • Mehmet Ali Aktürk

COMMON COUPLED FIXED POINT THEOREMS FOR GENERALIZED NONLINEAR CONTRACTIONS ON METRIC SPACES INVOLVING A GRAPH

Abstract

New generalized forms of Banach and Kannan type contractions have been described and some coupled coincidence and coupled common fixed point results have been established in the setting of metric space involving a graph. Our theorems extend and generalize many existing results in the literature. Furthermore, an application to integral equations is presented to affirm the importance.

Keywords

References

  1. [1] Lakshmikantham V. and Ciric L.B., (2009) Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis, Theory, Methods & Applications 70, 4341-4349.
  2. [2] Choudhury B. and Kundu A., (2010) A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Analysis, Theory, Methods & Applications 73, 2524-2531.
  3. [3] Geraghty M., (1973) On contractive mappings, Proceedings of the American Mathematical Society 40, 604-608.
  4. [4] Choudhury B.S. and Kundu A., (2012) On coupled generalised Banach and Kannan type contractions, Journal of Nonlinear Science and Applications 5, 259-270.
  5. [5] Kim J.K. and Chandok S., (2013) Coupled common fixed point theorems for generalized nonlinear contraction mappings with the mixed monotone property in partially ordered metric spaces, Fixed Point Theory and Applications 307, doi: 10.1186/1687-1812-2013-307.
  6. [6] Jachymski J., (2008) The contraction principle for mappings on a metric space with a graph, Proceedings of the American Mathematical Society 136, 1359-1373.
  7. [7] Beg I., Butt A.R., Radojevic S., (2010) The contraction principle for set valued mappings on a metric space with a graph, Computers & Mathematics with Applications 60, 1214-1219.
  8. [8] Bojor F., (2012) Fixed point theorems for Reich type contractions on metric space with a graph, Nonlinear Analysis, Theory, Methods & Applications 75 (9), 3895-3901.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Esra Yolaçan This is me
0000-0002-1655-0993
Türkiye

Mehmet Ali Aktürk This is me
0000-0001-9826-0844
Türkiye

Publication Date

June 1, 2018

Submission Date

March 13, 2017

Acceptance Date

April 13, 2018

Published in Issue

Year 2018 Volume: 36 Number: 2

APA
Yolaçan, E., Debnath, P., & Aktürk, M. A. (2018). COMMON COUPLED FIXED POINT THEOREMS FOR GENERALIZED NONLINEAR CONTRACTIONS ON METRIC SPACES INVOLVING A GRAPH. Sigma Journal of Engineering and Natural Sciences, 36(2), 419-432. https://izlik.org/JA39GB76TM
AMA
1.Yolaçan E, Debnath P, Aktürk MA. COMMON COUPLED FIXED POINT THEOREMS FOR GENERALIZED NONLINEAR CONTRACTIONS ON METRIC SPACES INVOLVING A GRAPH. SIGMA. 2018;36(2):419-432. https://izlik.org/JA39GB76TM
Chicago
Yolaçan, Esra, Pradip Debnath, and Mehmet Ali Aktürk. 2018. “COMMON COUPLED FIXED POINT THEOREMS FOR GENERALIZED NONLINEAR CONTRACTIONS ON METRIC SPACES INVOLVING A GRAPH”. Sigma Journal of Engineering and Natural Sciences 36 (2): 419-32. https://izlik.org/JA39GB76TM.
EndNote
Yolaçan E, Debnath P, Aktürk MA (June 1, 2018) COMMON COUPLED FIXED POINT THEOREMS FOR GENERALIZED NONLINEAR CONTRACTIONS ON METRIC SPACES INVOLVING A GRAPH. Sigma Journal of Engineering and Natural Sciences 36 2 419–432.
IEEE
[1]E. Yolaçan, P. Debnath, and M. A. Aktürk, “COMMON COUPLED FIXED POINT THEOREMS FOR GENERALIZED NONLINEAR CONTRACTIONS ON METRIC SPACES INVOLVING A GRAPH”, SIGMA, vol. 36, no. 2, pp. 419–432, June 2018, [Online]. Available: https://izlik.org/JA39GB76TM
ISNAD
Yolaçan, Esra - Debnath, Pradip - Aktürk, Mehmet Ali. “COMMON COUPLED FIXED POINT THEOREMS FOR GENERALIZED NONLINEAR CONTRACTIONS ON METRIC SPACES INVOLVING A GRAPH”. Sigma Journal of Engineering and Natural Sciences 36/2 (June 1, 2018): 419-432. https://izlik.org/JA39GB76TM.
JAMA
1.Yolaçan E, Debnath P, Aktürk MA. COMMON COUPLED FIXED POINT THEOREMS FOR GENERALIZED NONLINEAR CONTRACTIONS ON METRIC SPACES INVOLVING A GRAPH. SIGMA. 2018;36:419–432.
MLA
Yolaçan, Esra, et al. “COMMON COUPLED FIXED POINT THEOREMS FOR GENERALIZED NONLINEAR CONTRACTIONS ON METRIC SPACES INVOLVING A GRAPH”. Sigma Journal of Engineering and Natural Sciences, vol. 36, no. 2, June 2018, pp. 419-32, https://izlik.org/JA39GB76TM.
Vancouver
1.Esra Yolaçan, Pradip Debnath, Mehmet Ali Aktürk. COMMON COUPLED FIXED POINT THEOREMS FOR GENERALIZED NONLINEAR CONTRACTIONS ON METRIC SPACES INVOLVING A GRAPH. SIGMA [Internet]. 2018 Jun. 1;36(2):419-32. Available from: https://izlik.org/JA39GB76TM

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