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Fixed point results for Pata contraction on a metric space with a graph and its application

Yıl 2019, Cilt: 68 Sayı: 2, 1831 - 1840, 01.08.2019
https://doi.org/10.31801/cfsuasmas.467481

Öz

Let $(X,d)$ be a metric space endowed with a graph $G$ such that the set $V(G)$ of vertices of $G$ coincides with $X$‎. ‎We define the notion of Pata-$G$-contraction type maps and obtain some fixed point theorems for such mappings‎. ‎This extends and subsumes many recent results which were obtained for other contractive type mappings on a partially ordered metric space‎. ‎As an application‎, ‎we present theorem on the convergence of successive approximations for some linear operators on a Banach space‎.

Kaynakça

  • Abbas, M., Nazir, T., Popovic, B.Z., Radenovic, S., On weakly commuting set valued mappings on a domain of sets endowed with directed graph, to appear in Results in Mathematics, Doi: 10.1007/s00025-016-0588-x.
  • Aleomraninejad, S.M.A., Rezapour, S., Shahzad, N., Some fixed point results on a metric space with a graph, Topology and its Application, 159 (2011), 659-663.
  • Choudhury, B.S., Kadelburg, Z., Metiya, N., Radenovic, N., Survey of fixed point theorems under Pata-type contraction, too appear in Bull. of Malaysian Math. Soc. 2019.
  • Jacob , G.K., Khan, M.S., Park, C., Yun, S., On Generalized Pata Type Contractions, Mathematics, 6, 25, (2018), 1-8.
  • Johnsonbaugh, I.R., Discrete Mathematics, Prentice-Hall, Inc. New Jersey, 1997.
  • Kadelburg, Z., Radenovic, S., Fixed point theorems under Pata-type conditions in metric spaces, J. Egypt. Math. Soc., 24, (2016), 77â€"82.
  • Kadelburg, Z., Radenovic, S., Pata-type common fixed point results in b-metric and b-rectangular metric spaces, J. Nonlinear Sci. Appl., 8 (2015), 944-954.
  • Kadelburg, Z., Radenovic, S., A note on Pata-type cyclic contractions, Sarajevo Journal of Mathematics, 11 (24), No.2, (2015), 1-11.
  • Kadelburg, Z., Radenovic, S., Fixed point and tripled fixed point theorems under Pata-type contractions in ordered metric spaces, International Journal of Analysis and Applications, 6, No. 1 (2014), 113-122.
  • Kelisky, R.P., Rivlin, T.J., Iterates of Bernstein polynomials, Pacific J. Math., 21 (1967), 511-520.
  • Lukawska, G.G., Jachymski, J., IFS on a metric space with a graph structure and extension of the Kelisky-Rivlin theorem, J. Math. Anal. and Appl., 356(2), (2009). DOI: 10.1016/j.jmaa.2009.03.023.
  • Nazir, T., Abbas, M., Lampert, T. A., Radenovic, S., Common fixed points of set-valued F-contraction mappings on domain of sets endowed with directed graph, Comp. Appl. Math., DOI 10.1007/s40314-016-0314-z.
  • Pata, V., A fixed point theorem in metric spaces, J. Fixed Point Theory Appl., 10 (2011), 299-305.
  • Petrusel, A., Rus, I.A., Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc., 134 (2006), 411--418.
  • Rus, I.A., Iterates of Bernstein polynomials, via contraction principle, J. Math. Anal. Appl., 292 (2004), 259-261.
Yıl 2019, Cilt: 68 Sayı: 2, 1831 - 1840, 01.08.2019
https://doi.org/10.31801/cfsuasmas.467481

Öz

Kaynakça

  • Abbas, M., Nazir, T., Popovic, B.Z., Radenovic, S., On weakly commuting set valued mappings on a domain of sets endowed with directed graph, to appear in Results in Mathematics, Doi: 10.1007/s00025-016-0588-x.
  • Aleomraninejad, S.M.A., Rezapour, S., Shahzad, N., Some fixed point results on a metric space with a graph, Topology and its Application, 159 (2011), 659-663.
  • Choudhury, B.S., Kadelburg, Z., Metiya, N., Radenovic, N., Survey of fixed point theorems under Pata-type contraction, too appear in Bull. of Malaysian Math. Soc. 2019.
  • Jacob , G.K., Khan, M.S., Park, C., Yun, S., On Generalized Pata Type Contractions, Mathematics, 6, 25, (2018), 1-8.
  • Johnsonbaugh, I.R., Discrete Mathematics, Prentice-Hall, Inc. New Jersey, 1997.
  • Kadelburg, Z., Radenovic, S., Fixed point theorems under Pata-type conditions in metric spaces, J. Egypt. Math. Soc., 24, (2016), 77â€"82.
  • Kadelburg, Z., Radenovic, S., Pata-type common fixed point results in b-metric and b-rectangular metric spaces, J. Nonlinear Sci. Appl., 8 (2015), 944-954.
  • Kadelburg, Z., Radenovic, S., A note on Pata-type cyclic contractions, Sarajevo Journal of Mathematics, 11 (24), No.2, (2015), 1-11.
  • Kadelburg, Z., Radenovic, S., Fixed point and tripled fixed point theorems under Pata-type contractions in ordered metric spaces, International Journal of Analysis and Applications, 6, No. 1 (2014), 113-122.
  • Kelisky, R.P., Rivlin, T.J., Iterates of Bernstein polynomials, Pacific J. Math., 21 (1967), 511-520.
  • Lukawska, G.G., Jachymski, J., IFS on a metric space with a graph structure and extension of the Kelisky-Rivlin theorem, J. Math. Anal. and Appl., 356(2), (2009). DOI: 10.1016/j.jmaa.2009.03.023.
  • Nazir, T., Abbas, M., Lampert, T. A., Radenovic, S., Common fixed points of set-valued F-contraction mappings on domain of sets endowed with directed graph, Comp. Appl. Math., DOI 10.1007/s40314-016-0314-z.
  • Pata, V., A fixed point theorem in metric spaces, J. Fixed Point Theory Appl., 10 (2011), 299-305.
  • Petrusel, A., Rus, I.A., Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc., 134 (2006), 411--418.
  • Rus, I.A., Iterates of Bernstein polynomials, via contraction principle, J. Math. Anal. Appl., 292 (2004), 259-261.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Maryam Ramezani 0000-0002-5593-1924

Asma Arian Bu kişi benim 0000-0002-5593-1924

Yayımlanma Tarihi 1 Ağustos 2019
Gönderilme Tarihi 5 Ekim 2018
Kabul Tarihi 26 Mart 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 68 Sayı: 2

Kaynak Göster

APA Ramezani, M., & Arian, A. (2019). Fixed point results for Pata contraction on a metric space with a graph and its application. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1831-1840. https://doi.org/10.31801/cfsuasmas.467481
AMA Ramezani M, Arian A. Fixed point results for Pata contraction on a metric space with a graph and its application. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Ağustos 2019;68(2):1831-1840. doi:10.31801/cfsuasmas.467481
Chicago Ramezani, Maryam, ve Asma Arian. “Fixed Point Results for Pata Contraction on a Metric Space With a Graph and Its Application”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, sy. 2 (Ağustos 2019): 1831-40. https://doi.org/10.31801/cfsuasmas.467481.
EndNote Ramezani M, Arian A (01 Ağustos 2019) Fixed point results for Pata contraction on a metric space with a graph and its application. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1831–1840.
IEEE M. Ramezani ve A. Arian, “Fixed point results for Pata contraction on a metric space with a graph and its application”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 68, sy. 2, ss. 1831–1840, 2019, doi: 10.31801/cfsuasmas.467481.
ISNAD Ramezani, Maryam - Arian, Asma. “Fixed Point Results for Pata Contraction on a Metric Space With a Graph and Its Application”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (Ağustos 2019), 1831-1840. https://doi.org/10.31801/cfsuasmas.467481.
JAMA Ramezani M, Arian A. Fixed point results for Pata contraction on a metric space with a graph and its application. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1831–1840.
MLA Ramezani, Maryam ve Asma Arian. “Fixed Point Results for Pata Contraction on a Metric Space With a Graph and Its Application”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 68, sy. 2, 2019, ss. 1831-40, doi:10.31801/cfsuasmas.467481.
Vancouver Ramezani M, Arian A. Fixed point results for Pata contraction on a metric space with a graph and its application. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1831-40.

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

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