A Common Fixed Point Theorem for Generalized Weakly Contractive Mappings in Multiplicative Metric Spaces
Year 2020,
, 1 - 13, 31.03.2020
Kidane Koyas
,
Alemayehu Gebre
,
Aynalem Kassaye
Abstract
In this paper, we introduced generalized weakly contractive mappings, established a common fixed point result and proved the
existence and uniqueness of a common fixed point. Finally, we provide
an example in support of our main finding.
Supporting Institution
Jimma University
Thanks
Jimma University is gratefully acknowledged for material support.
References
- [1] M. Abbas, B. Ali, Yi Suleiman, Common fixed points of locally contractive mappingsin multiplicative metric spaces with applications, Int. J., Math. Math. Sci. 2015, Article ID 218683, (2015).
- [2] M. Abbas, M. De La Sen, T. Nazir, Common fixed points of generalized rationaltype cocyclic mappings in multiplicative metric spaces, Discrete Dyn. Nat. Soc. 2015,Article Id 532725, (2015).
- [3] Y.I. Alber, and S. Guerre-Delabriere, Principle of weakly contractive maps in Hilbertspace, New Results in Operator Theory, Advances and Applications.I. Gohberg andY. Lyubich, Eds., 98, 7 − 22, (1997).
- [4] S. Banach, Sur les opérations dans les ensembles abstraits et leur application auxéquations intégrales, Fundam. Math.,3, 133-181, (1922).
- [5] A. Bashirov, E. Kurpinar, A. Ozyapici, Multiplicative calculus and its applications, J.Math. Anal. Appl. 337 (1), 36-48, (2008).
- [6] A.E. Bashirov, E. Misirli, Y. Tandogdu, and A. Ozyapici, On modeling with multiplicative differential equations, Applied Mathematics-A Journal of Chinese Universities, 26, 425 − 438, (2011)
- [7] S.K. Chatterjea, Fixed point theorems, Computes.Rend. Acad, Bulgaria Sci. 25, 727-730, (1972).
- [8] S. Cho, Fixed point theorems for generalized weakly contractive mappings in metricspaces with applications, Fixed Point Theory and Applications, (2018).
- [9] B.S. Choudhury, P. Konar, B.E. Rhoades, N. Metiya, Fixed point theorems for generalized weakly contractive mappings, Nonlinear Anal. 74, 2116-2126, (2011).
- [10] L. Florack and H. van Assen, Multiplicative calculus in biomedical image analysis,Journal of Mathematical Imaging and Vision, 42(1), 64 − 75, (2012).
- [11] M. Grossman, and R. Katz, Non-Newtonian Calculus, Lee Press,Pigeon Cove, (1972).
- [12] X. He, M. Song, and D. Chen, Common fixed points for weak commutative mappingson a multiplicative metric space, Fixed Point Theory and Applications, 48, (2014).
- [13] G.Jungck, Common fixed points for noncontinuous nonself mappings on nonmetricspaces, Far EastJ. Math. Sci.4(2), 199âĂŞ212, (1996).
- [14] R. Kannan, Some results on fixed points, Bull. Cal. Math., 60, 71-76, (1968).
- [15] S.M. Kang, P. Kumar, S. Kumar, P. Nagpal, S.K. Garg, Common fixed points forcompatible mappings and its variants in multiplicative metric spaces, Int. J. PureAppl. Math., 102(2), 383-406, (2015).
- [16] M. Özavsar, A. C. Cevikel, Fixed points of multiplicative contraction mappings onmultiplicative metric spaces, http://arxiv.org/abs/1205.5131v1, (2012).
- [17] M. Sarwar, and R. Badshah-e, Some unique fixed point theorems in multiplicativemetric space, arXiv:1410.3384v2 [math.GM], (2014).
- [18] T. Zamfirescu, Fixed Point Theorems in Metric Spaces, Arch. Math. (Basel), 23,292-298, (1972).
Year 2020,
, 1 - 13, 31.03.2020
Kidane Koyas
,
Alemayehu Gebre
,
Aynalem Kassaye
References
- [1] M. Abbas, B. Ali, Yi Suleiman, Common fixed points of locally contractive mappingsin multiplicative metric spaces with applications, Int. J., Math. Math. Sci. 2015, Article ID 218683, (2015).
- [2] M. Abbas, M. De La Sen, T. Nazir, Common fixed points of generalized rationaltype cocyclic mappings in multiplicative metric spaces, Discrete Dyn. Nat. Soc. 2015,Article Id 532725, (2015).
- [3] Y.I. Alber, and S. Guerre-Delabriere, Principle of weakly contractive maps in Hilbertspace, New Results in Operator Theory, Advances and Applications.I. Gohberg andY. Lyubich, Eds., 98, 7 − 22, (1997).
- [4] S. Banach, Sur les opérations dans les ensembles abstraits et leur application auxéquations intégrales, Fundam. Math.,3, 133-181, (1922).
- [5] A. Bashirov, E. Kurpinar, A. Ozyapici, Multiplicative calculus and its applications, J.Math. Anal. Appl. 337 (1), 36-48, (2008).
- [6] A.E. Bashirov, E. Misirli, Y. Tandogdu, and A. Ozyapici, On modeling with multiplicative differential equations, Applied Mathematics-A Journal of Chinese Universities, 26, 425 − 438, (2011)
- [7] S.K. Chatterjea, Fixed point theorems, Computes.Rend. Acad, Bulgaria Sci. 25, 727-730, (1972).
- [8] S. Cho, Fixed point theorems for generalized weakly contractive mappings in metricspaces with applications, Fixed Point Theory and Applications, (2018).
- [9] B.S. Choudhury, P. Konar, B.E. Rhoades, N. Metiya, Fixed point theorems for generalized weakly contractive mappings, Nonlinear Anal. 74, 2116-2126, (2011).
- [10] L. Florack and H. van Assen, Multiplicative calculus in biomedical image analysis,Journal of Mathematical Imaging and Vision, 42(1), 64 − 75, (2012).
- [11] M. Grossman, and R. Katz, Non-Newtonian Calculus, Lee Press,Pigeon Cove, (1972).
- [12] X. He, M. Song, and D. Chen, Common fixed points for weak commutative mappingson a multiplicative metric space, Fixed Point Theory and Applications, 48, (2014).
- [13] G.Jungck, Common fixed points for noncontinuous nonself mappings on nonmetricspaces, Far EastJ. Math. Sci.4(2), 199âĂŞ212, (1996).
- [14] R. Kannan, Some results on fixed points, Bull. Cal. Math., 60, 71-76, (1968).
- [15] S.M. Kang, P. Kumar, S. Kumar, P. Nagpal, S.K. Garg, Common fixed points forcompatible mappings and its variants in multiplicative metric spaces, Int. J. PureAppl. Math., 102(2), 383-406, (2015).
- [16] M. Özavsar, A. C. Cevikel, Fixed points of multiplicative contraction mappings onmultiplicative metric spaces, http://arxiv.org/abs/1205.5131v1, (2012).
- [17] M. Sarwar, and R. Badshah-e, Some unique fixed point theorems in multiplicativemetric space, arXiv:1410.3384v2 [math.GM], (2014).
- [18] T. Zamfirescu, Fixed Point Theorems in Metric Spaces, Arch. Math. (Basel), 23,292-298, (1972).