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.