Abstract
The aim of this paper is to generalize celebrated results due to Wardowski[8, 9] and also to provide yet new solutions to the once open problem[6, p.242] on the existence of a contractive mapping which possesses a fixed point but is not continuous at the fixed point via generalized F**-weak contractions. Finally, an example is given to illustrate our results.
The aim of this paper is to generalize celebrated results due to Wardowski[8, 9] and also to provide yet new solutions to the once open problem[6, p.242] on the existence of a contractive mapping which possesses a fixed point but is not continuous at the fixed point via generalized F**-weak contractions. Finally, an example is given to illustrate our results.
Keywords
F-contraction F-weak contraction F**-weak contraction contractive mapping fixed point theorem discontinuity at the fi xed point
References
- [1] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math, 3(1) (1922), 133-181.
- [2] M. Berzig, E. Karapinar, A. F. Roldan-Lopez-de Hierro, Discussion on generalized-(alpha psi , beta )-contractive mappings via generalized altering distance function and related fixed point theorems, Abstr. Appl. Anal., 2014, 1-12.
- [3] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 60 (1968), 71-76.
- [4] R. Pant, Discontinuity and fixed points, J. Math. Anal. Appl., 240(1) (1999), 284-289.
- [5] B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Am. Math. Soc., 226 (1977), 257-290.
- [6] B.E. Rhoades, Contractive definitions and continuity, Contemp. Math., 72 (1988), 233-245.
- [7] W.M. Alfaqih, M. Imdad and R. Gubran, An observation on F-weak contractions and discontinuity at the fixed point with an application, J. Fixed Point Theory Appl., 22(3) (2020).
- [8] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl.,94(6) (2012).
- [9] D. Wardowski, N.V. Dung, Fixed points of F-weak contractions on complete metric spaces, Demonstr. Math., 47(1) (2014), 146-155
Abstract
References
- [1] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math, 3(1) (1922), 133-181.
- [2] M. Berzig, E. Karapinar, A. F. Roldan-Lopez-de Hierro, Discussion on generalized-(alpha psi , beta )-contractive mappings via generalized altering distance function and related fixed point theorems, Abstr. Appl. Anal., 2014, 1-12.
- [3] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 60 (1968), 71-76.
- [4] R. Pant, Discontinuity and fixed points, J. Math. Anal. Appl., 240(1) (1999), 284-289.
- [5] B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Am. Math. Soc., 226 (1977), 257-290.
- [6] B.E. Rhoades, Contractive definitions and continuity, Contemp. Math., 72 (1988), 233-245.
- [7] W.M. Alfaqih, M. Imdad and R. Gubran, An observation on F-weak contractions and discontinuity at the fixed point with an application, J. Fixed Point Theory Appl., 22(3) (2020).
- [8] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl.,94(6) (2012).
- [9] D. Wardowski, N.V. Dung, Fixed points of F-weak contractions on complete metric spaces, Demonstr. Math., 47(1) (2014), 146-155
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Articles |
| Authors | |
| Publication Date | December 30, 2020 |
| Published in Issue | Year 2020 Volume: 4 Issue: 4 |