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Fixed Point Theorems on Partial Metric Spaces Involving Rational Type Expressions with C-Class Functions

Year 2017, Volume: 7, 1 - 9, 19.12.2017

İsa Yildirim Arslan Hojat Ansarı M. S. Khan Brian Fısher

Abstract

In this paper, we present some fixed point theorems for contraction of rational type by using a class of pairs of functions satisfying certain assumptions with C-class functions in a complete partial metric space. Also, an example is given to support our main result. Our result extends and generalizes some well-known results of [7] and [8] in metric spaces.

Keywords

Partial metric space rational type contraction fixed point rational type contraction C-class function

References

  • Abbas, M., Nazir, T., Ramaguera, S., Fixed point results for generalized cyclic contraction mappings in partial metric spaces, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat., RACSAM, 106(1)(2012), 287–297.
  • Abdeljawad, T., Karapinar, E., Tas, K., Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett., 24(11)(2011), 1900–1904.
  • Acar, O., Berinde, V., Altun, I., Fixed point theorems for Ciric-type strong almost contractions on partial metric spaces, J. Fixed Point Theory Appl., 12(2012), 247–259.
  • Ansari, A. H., Note on $\varphi $--$\psi $ contractive type mappings and related fixed point, The 2nd Regional Conference on Mathematics And Applications, PNU, September 2014, 377–380.
  • Ansari, A. H., Chandok, S., Ionescu, C., Fixed point theorems on b-metric spaces for weak contractions with auxiliary functions, Journal of Inequalities and Applications 2014, 2014:429, 17 pages.
  • Dass, B. K., Gupta, S., An extension of Banach contraction principle through rational expressions, Indian J. Pure Appl. Math., 6(1975), 1455–1458.
  • Dutta, P. N., Choudhury, B. S., A generalization of contraction principle in metric spaces, Fixed Point Theory Appl., 2008, Article ID 406368.
  • Erhan, D. M., Karapinar, E., Narang, T. D., Different types of Meir-Keeler contractions on partial metric spaces, J. Comput. Anal. Appl., 14(6)(2012), 1000–1005.
  • Hoxha, E., Ansari, A. H., Zoto, K., Some common fixed point results through generalized altering distances on dislocated metric spaces, Proceedings of EIIC, September 1-5, 2014, pages 403–409.
  • Karapinar, E., Weak $\phi $-contraction on partial metric spaces, J. Computr. Anal. Appl., 14(2)(2012), 206–210.
  • Karapinar, E., Shatanawi, W., Tas, K., Fixed point theorems on partial metric spaces involving rational expressions, Miskolc Math. Notes, 14(2013), 135–142.
  • Karapinar, E., Erhan, I. M., Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett., 24(2011), 1894–1899.
  • Karapinar, E., Generalization of Caristi-Kirk’s theorem on partial metric spaces, Fixed Point Theory Appl., 2011(4)(2011), doi.org/10.1186/1687-1812-2011-4.
  • Khan, M. S., Swaleh, M., Sessa, S., Fixed point theorems by altering distances between the points, Bulletin of the Australian Mathematical Society, 30(1)(1984), 1–9.
  • Matthews, S. G., Partial metric topology, Dept. of Computer Science, University of Warwick, Research Report, 212, 1992.
  • Matthews, S. G., Partial metric topology, in Papers on general topology and applications, Ser. Papers from the 8th summer conference at Queens College, New York, NY, USA, June 18-20, 1992, S. Andima, Ed. New York: The New York Academy of Sciences, 728(1994), 183–197.
  • Oltra, S., Olero, O., Banach’s fixed point theorem for partial metric spaces, Rend. Ist. Mat. Univ. Trieste, 36(1-2)(2004), 17–26.
  • Saluja, A. S., Khan, M. S., Jhade, P. K., Fisher, B., Some fixed point theorems for mappings involving rational type expressions in partial metric spaces, Applied Mathematics E-Notes, 15(2015), 147–161.
  • Valero, O., On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topl., 6(2)(2005), 229–240.

Year 2017, Volume: 7, 1 - 9, 19.12.2017

İsa Yildirim Arslan Hojat Ansarı M. S. Khan Brian Fısher

Abstract

References

  • Abbas, M., Nazir, T., Ramaguera, S., Fixed point results for generalized cyclic contraction mappings in partial metric spaces, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat., RACSAM, 106(1)(2012), 287–297.
  • Abdeljawad, T., Karapinar, E., Tas, K., Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett., 24(11)(2011), 1900–1904.
  • Acar, O., Berinde, V., Altun, I., Fixed point theorems for Ciric-type strong almost contractions on partial metric spaces, J. Fixed Point Theory Appl., 12(2012), 247–259.
  • Ansari, A. H., Note on $\varphi $--$\psi $ contractive type mappings and related fixed point, The 2nd Regional Conference on Mathematics And Applications, PNU, September 2014, 377–380.
  • Ansari, A. H., Chandok, S., Ionescu, C., Fixed point theorems on b-metric spaces for weak contractions with auxiliary functions, Journal of Inequalities and Applications 2014, 2014:429, 17 pages.
  • Dass, B. K., Gupta, S., An extension of Banach contraction principle through rational expressions, Indian J. Pure Appl. Math., 6(1975), 1455–1458.
  • Dutta, P. N., Choudhury, B. S., A generalization of contraction principle in metric spaces, Fixed Point Theory Appl., 2008, Article ID 406368.
  • Erhan, D. M., Karapinar, E., Narang, T. D., Different types of Meir-Keeler contractions on partial metric spaces, J. Comput. Anal. Appl., 14(6)(2012), 1000–1005.
  • Hoxha, E., Ansari, A. H., Zoto, K., Some common fixed point results through generalized altering distances on dislocated metric spaces, Proceedings of EIIC, September 1-5, 2014, pages 403–409.
  • Karapinar, E., Weak $\phi $-contraction on partial metric spaces, J. Computr. Anal. Appl., 14(2)(2012), 206–210.
  • Karapinar, E., Shatanawi, W., Tas, K., Fixed point theorems on partial metric spaces involving rational expressions, Miskolc Math. Notes, 14(2013), 135–142.
  • Karapinar, E., Erhan, I. M., Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett., 24(2011), 1894–1899.
  • Karapinar, E., Generalization of Caristi-Kirk’s theorem on partial metric spaces, Fixed Point Theory Appl., 2011(4)(2011), doi.org/10.1186/1687-1812-2011-4.
  • Khan, M. S., Swaleh, M., Sessa, S., Fixed point theorems by altering distances between the points, Bulletin of the Australian Mathematical Society, 30(1)(1984), 1–9.
  • Matthews, S. G., Partial metric topology, Dept. of Computer Science, University of Warwick, Research Report, 212, 1992.
  • Matthews, S. G., Partial metric topology, in Papers on general topology and applications, Ser. Papers from the 8th summer conference at Queens College, New York, NY, USA, June 18-20, 1992, S. Andima, Ed. New York: The New York Academy of Sciences, 728(1994), 183–197.
  • Oltra, S., Olero, O., Banach’s fixed point theorem for partial metric spaces, Rend. Ist. Mat. Univ. Trieste, 36(1-2)(2004), 17–26.
  • Saluja, A. S., Khan, M. S., Jhade, P. K., Fisher, B., Some fixed point theorems for mappings involving rational type expressions in partial metric spaces, Applied Mathematics E-Notes, 15(2015), 147–161.
  • Valero, O., On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topl., 6(2)(2005), 229–240.
There are 19 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

İsa Yildirim

Arslan Hojat Ansarı

M. S. Khan This is me

Brian Fısher This is me

Publication Date December 19, 2017
Published in Issue Year 2017 Volume: 7

Cite

APA Yildirim, İ., Ansarı, A. H., Khan, M. S., Fısher, B. (2017). Fixed Point Theorems on Partial Metric Spaces Involving Rational Type Expressions with C-Class Functions. Turkish Journal of Mathematics and Computer Science, 7, 1-9.
AMA Yildirim İ, Ansarı AH, Khan MS, Fısher B. Fixed Point Theorems on Partial Metric Spaces Involving Rational Type Expressions with C-Class Functions. TJMCS. December 2017;7:1-9.
Chicago Yildirim, İsa, Arslan Hojat Ansarı, M. S. Khan, and Brian Fısher. “Fixed Point Theorems on Partial Metric Spaces Involving Rational Type Expressions With C-Class Functions”. Turkish Journal of Mathematics and Computer Science 7, December (December 2017): 1-9.
EndNote Yildirim İ, Ansarı AH, Khan MS, Fısher B (December 1, 2017) Fixed Point Theorems on Partial Metric Spaces Involving Rational Type Expressions with C-Class Functions. Turkish Journal of Mathematics and Computer Science 7 1–9.
IEEE İ. Yildirim, A. H. Ansarı, M. S. Khan, and B. Fısher, “Fixed Point Theorems on Partial Metric Spaces Involving Rational Type Expressions with C-Class Functions”, TJMCS, vol. 7, pp. 1–9, 2017.
ISNAD Yildirim, İsa et al. “Fixed Point Theorems on Partial Metric Spaces Involving Rational Type Expressions With C-Class Functions”. Turkish Journal of Mathematics and Computer Science 7 (December 2017), 1-9.
JAMA Yildirim İ, Ansarı AH, Khan MS, Fısher B. Fixed Point Theorems on Partial Metric Spaces Involving Rational Type Expressions with C-Class Functions. TJMCS. 2017;7:1–9.
MLA Yildirim, İsa et al. “Fixed Point Theorems on Partial Metric Spaces Involving Rational Type Expressions With C-Class Functions”. Turkish Journal of Mathematics and Computer Science, vol. 7, 2017, pp. 1-9.
Vancouver Yildirim İ, Ansarı AH, Khan MS, Fısher B. Fixed Point Theorems on Partial Metric Spaces Involving Rational Type Expressions with C-Class Functions. TJMCS. 2017;7:1-9.