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A Common Fixed Point Theorem for Generalized Weakly Contractive Mappings in Multiplicative Metric Spaces

Yıl 2020, Cilt: 4 Sayı: 1, 1 - 13, 31.03.2020
https://doi.org/10.31197/atnaa.573903

Öz

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.


Destekleyen Kurum

Jimma University

Teşekkür

Jimma University is gratefully acknowledged for material support.

Kaynakça

  • [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).
Yıl 2020, Cilt: 4 Sayı: 1, 1 - 13, 31.03.2020
https://doi.org/10.31197/atnaa.573903

Öz

Kaynakça

  • [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).
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Kidane Koyas

Alemayehu Gebre

Aynalem Kassaye Bu kişi benim

Yayımlanma Tarihi 31 Mart 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 4 Sayı: 1

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