Research Article
BibTex RIS Cite
Year 2019, Volume: 68 Issue: 2, 1694 - 1708, 01.08.2019
https://doi.org/10.31801/cfsuasmas.425424

Abstract

References

  • Ansari, A.H. , Note on ϕ-ψ- -contractive type mappings and related fixed point, The 2nd Regional Conference on Mathematics and Applications, Payame Noor University (2014), 377--380.
  • Dhage, B.C., Generalized metric spaces and mapping with fixed point, Bull. Calcutta Math. Soc. 84 (1992), 329--336.
  • Fisher, B., A fixed point mapping, Bull. Calcutta Math. Soc. 68 (1976), 265--266.
  • Delbosco, D., Un'estensione di un teorema sul punto di S. Reich, Rend. Sem. Mat. Univers. Politecn. Torino 35 (1967), 233--238.
  • Guo, D. and Lakshmikantham, V., Coupled fixed points of nonlinear operators with applications, Nonlinear Analysis 11 (1987), 623--632.
  • Skof, F., Teorema di punti fisso per applicazioni negli spazi metrici, Atti Accad. Sci. Torino 111 (1977), 323--329.
  • Babu, G.V.R. and Sailaja, P.D., A fixed point theorem of generalized weakly contractive maps in orbitally complete metric spaces, Thai Journal of Mathematics 9(1) (2011), 1--10.
  • Sastry, K.P.R., Babu, G.V.R. and Rao, D.N., Fixed point theorem in complete metric space by using a continuous control function, Bull. Cal. Math. Soc. 91(6) (1999), 493--502.
  • Sastry, K.P.R., Naidu, S.V.R., Babu, G.V.R. and Naidu, G.A., Generalization of common fixed point theorems for weakly commuting maps by altering distances, Tamkang J. Math. 31(3) (2000), 243--250.
  • Gordji, M.E., Akbartabar, E., Cho, Y.J. and Remezani, M., Coupled common fixed point theorems for mixed weakly monotone mappings in partially ordered metric spaces, Fixed Point Theory and Applications 95 (2012), Article ID:95.
  • Khan, M.S., Swalesh, M. and Sessa, S., Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc. 30 (1984), 323--326.
  • Dung, N.V., On coupled common fixed points for mixed weakly monotone maps in partially ordered S -metric spaces, Fixed Point Theory and Applications 48 (2013), 17 pages.
  • Mani, N., Existence of fixed points and their applications in certain spaces [Ph.D.Thesis], M. M. University, Mullana, Ambala, India, 2017.
  • Mani, N., Generalized C_{β}^{ψ} -rational contraction and fixed point theorem with application to second order differential equation, Mathematica Moravica 22(1) (2018), 43--54.
  • Marr, R. D., Partially ordered space and metric spaces, American Mathematical Monthly 72(6) (1965), 628--631.
  • Gahler, S., 2-metricsche Raume und ihre topologische structure, Math. Nachr. 26 (1963), 115--148.
  • Sedghi, S., Shobe, N. and Zhou, H., A common fixed point theorem in D -metric spaces, Fixed Point theory and Application 2007 (2007), Article ID 27906, 13 pages.
  • Sedghi, S. and Shobe, N., A common unique random fixed point theorems in S -metric spaces, Journal of Prime Research in Mathematics 7 (2011), 25--34.
  • Sedghi, S. and Shobe, N. and Aliouche, A., A generalizations of fixed point theorems in S -metric spaces, Matematnhpn Bechnk 64 (2012), no. 3, 258--266.
  • Chang, S.S., Cho, Y.J. and Huang, N.J., Coupled fixed point theorems with applications, J. Korean Math. Soc. 33 (1996), no. 3, 575--585.
  • Gupta, V. and Mani, N., Common fixed point for two self-maps satisfying a generalized ^{ψ}∫_{φ} weakly contractive condition of integral type, International Journal of Nonlinear Science, 16(1) (2013), 64--71.
  • Gupta, V., Ramandeep, Mani, N. and Tripathi, A. K., Some fixed point result involving generalized altering distance function, Procedia Computer Science 79 (2016), 112--117.
  • Gupta, V., Shatanawi, W. and Mani, N., Fixed point theorems for (ψ,β) -Geraghty contraction type maps in ordered metric spaces and some applications to integral and ordinary differential equations, J. Fixed Point Theory Appl. 19(2) (2016), 1251--1267.
  • Lakshmikantham, V. and Ciric, L., Coupled common fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis 70 (2009), 4341--4349.
  • Chen, Y.Z., Existence theorems of coupled fixed points, J. Math. Anal. Appl. 154 (1991), 142--150.
  • Mustafa, Z. and Sims, B., A new approach to generalized metric spaces, J. Nonlinear and Convex Anal. 7(2) (2006), 289--297.

C-class functions on some coupled fixed point theorems in partially ordered S-metric spaces

Year 2019, Volume: 68 Issue: 2, 1694 - 1708, 01.08.2019
https://doi.org/10.31801/cfsuasmas.425424

Abstract

In this paper, we prove fixed point results employing mixed weakly monotone maps, C-class functions and altering distance function in the framework of S-metric space. Here, integral application has additionally been given.

References

  • Ansari, A.H. , Note on ϕ-ψ- -contractive type mappings and related fixed point, The 2nd Regional Conference on Mathematics and Applications, Payame Noor University (2014), 377--380.
  • Dhage, B.C., Generalized metric spaces and mapping with fixed point, Bull. Calcutta Math. Soc. 84 (1992), 329--336.
  • Fisher, B., A fixed point mapping, Bull. Calcutta Math. Soc. 68 (1976), 265--266.
  • Delbosco, D., Un'estensione di un teorema sul punto di S. Reich, Rend. Sem. Mat. Univers. Politecn. Torino 35 (1967), 233--238.
  • Guo, D. and Lakshmikantham, V., Coupled fixed points of nonlinear operators with applications, Nonlinear Analysis 11 (1987), 623--632.
  • Skof, F., Teorema di punti fisso per applicazioni negli spazi metrici, Atti Accad. Sci. Torino 111 (1977), 323--329.
  • Babu, G.V.R. and Sailaja, P.D., A fixed point theorem of generalized weakly contractive maps in orbitally complete metric spaces, Thai Journal of Mathematics 9(1) (2011), 1--10.
  • Sastry, K.P.R., Babu, G.V.R. and Rao, D.N., Fixed point theorem in complete metric space by using a continuous control function, Bull. Cal. Math. Soc. 91(6) (1999), 493--502.
  • Sastry, K.P.R., Naidu, S.V.R., Babu, G.V.R. and Naidu, G.A., Generalization of common fixed point theorems for weakly commuting maps by altering distances, Tamkang J. Math. 31(3) (2000), 243--250.
  • Gordji, M.E., Akbartabar, E., Cho, Y.J. and Remezani, M., Coupled common fixed point theorems for mixed weakly monotone mappings in partially ordered metric spaces, Fixed Point Theory and Applications 95 (2012), Article ID:95.
  • Khan, M.S., Swalesh, M. and Sessa, S., Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc. 30 (1984), 323--326.
  • Dung, N.V., On coupled common fixed points for mixed weakly monotone maps in partially ordered S -metric spaces, Fixed Point Theory and Applications 48 (2013), 17 pages.
  • Mani, N., Existence of fixed points and their applications in certain spaces [Ph.D.Thesis], M. M. University, Mullana, Ambala, India, 2017.
  • Mani, N., Generalized C_{β}^{ψ} -rational contraction and fixed point theorem with application to second order differential equation, Mathematica Moravica 22(1) (2018), 43--54.
  • Marr, R. D., Partially ordered space and metric spaces, American Mathematical Monthly 72(6) (1965), 628--631.
  • Gahler, S., 2-metricsche Raume und ihre topologische structure, Math. Nachr. 26 (1963), 115--148.
  • Sedghi, S., Shobe, N. and Zhou, H., A common fixed point theorem in D -metric spaces, Fixed Point theory and Application 2007 (2007), Article ID 27906, 13 pages.
  • Sedghi, S. and Shobe, N., A common unique random fixed point theorems in S -metric spaces, Journal of Prime Research in Mathematics 7 (2011), 25--34.
  • Sedghi, S. and Shobe, N. and Aliouche, A., A generalizations of fixed point theorems in S -metric spaces, Matematnhpn Bechnk 64 (2012), no. 3, 258--266.
  • Chang, S.S., Cho, Y.J. and Huang, N.J., Coupled fixed point theorems with applications, J. Korean Math. Soc. 33 (1996), no. 3, 575--585.
  • Gupta, V. and Mani, N., Common fixed point for two self-maps satisfying a generalized ^{ψ}∫_{φ} weakly contractive condition of integral type, International Journal of Nonlinear Science, 16(1) (2013), 64--71.
  • Gupta, V., Ramandeep, Mani, N. and Tripathi, A. K., Some fixed point result involving generalized altering distance function, Procedia Computer Science 79 (2016), 112--117.
  • Gupta, V., Shatanawi, W. and Mani, N., Fixed point theorems for (ψ,β) -Geraghty contraction type maps in ordered metric spaces and some applications to integral and ordinary differential equations, J. Fixed Point Theory Appl. 19(2) (2016), 1251--1267.
  • Lakshmikantham, V. and Ciric, L., Coupled common fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis 70 (2009), 4341--4349.
  • Chen, Y.Z., Existence theorems of coupled fixed points, J. Math. Anal. Appl. 154 (1991), 142--150.
  • Mustafa, Z. and Sims, B., A new approach to generalized metric spaces, J. Nonlinear and Convex Anal. 7(2) (2006), 289--297.
There are 26 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences, Applied Mathematics
Journal Section Review Articles
Authors

Vishal Gupta 0000-0001-9727-2827

Arslan Hojat Ansari 0000-0002-5527-1284

Naveen Mani This is me 0000-0002-7131-2664

Publication Date August 1, 2019
Submission Date May 21, 2018
Acceptance Date January 2, 2019
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Gupta, V., Ansari, A. H., & Mani, N. (2019). C-class functions on some coupled fixed point theorems in partially ordered S-metric spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1694-1708. https://doi.org/10.31801/cfsuasmas.425424
AMA Gupta V, Ansari AH, Mani N. C-class functions on some coupled fixed point theorems in partially ordered S-metric spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1694-1708. doi:10.31801/cfsuasmas.425424
Chicago Gupta, Vishal, Arslan Hojat Ansari, and Naveen Mani. “C-Class Functions on Some Coupled Fixed Point Theorems in Partially Ordered S-Metric Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1694-1708. https://doi.org/10.31801/cfsuasmas.425424.
EndNote Gupta V, Ansari AH, Mani N (August 1, 2019) C-class functions on some coupled fixed point theorems in partially ordered S-metric spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1694–1708.
IEEE V. Gupta, A. H. Ansari, and N. Mani, “C-class functions on some coupled fixed point theorems in partially ordered S-metric spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1694–1708, 2019, doi: 10.31801/cfsuasmas.425424.
ISNAD Gupta, Vishal et al. “C-Class Functions on Some Coupled Fixed Point Theorems in Partially Ordered S-Metric Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1694-1708. https://doi.org/10.31801/cfsuasmas.425424.
JAMA Gupta V, Ansari AH, Mani N. C-class functions on some coupled fixed point theorems in partially ordered S-metric spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1694–1708.
MLA Gupta, Vishal et al. “C-Class Functions on Some Coupled Fixed Point Theorems in Partially Ordered S-Metric Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1694-08, doi:10.31801/cfsuasmas.425424.
Vancouver Gupta V, Ansari AH, Mani N. C-class functions on some coupled fixed point theorems in partially ordered S-metric spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1694-708.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.