A generalized fixed point theorem in non-Newtonian calculus

Year 2017, Volume: 5 Issue: 4, 52 - 57, 01.10.2017

Mehmet Kir

Abstract

In this
paper, a generalized fixed point theorem and its results are established in the
concept of multiplicative distance which was introduced by Agamirza et.al [3]
to improve the non-Newtonian calculus. Our results include some existing
results in the concept of multiplicative metric space.

Keywords

Fixed point, multiplicative distance, multiplicative metric

References

• M. Grossman, R. Kantz, Non-Newtonian Calculus, Lee Press, Pigeon Cove, MA, 1972.
• D. Stanley, A multiplicative calculus, Primus IX (4)1999,310-326.
• Agamirza E. Bashirov, Emine. M. Kurpınar, A. Özyapıcı, Multiplicative calculus and its applications, J. Math. Anal. Appl. 337(2008)36-48.
• L. Florack, H. van Assen, Multiplicative calculus in Biomedical image analysis, J. Math. Imaging Vis. (2012) 42: 64-75.
• M., Özsavar and A. C. Çevikel, Fixed point of multipcative contraction mappings on multiplicative metric space. arXiv:1205.5131v1[matn.GN] (2012).
• M. Sarwar and Badshah-e-Rome, Some unique fixed point theorems in multiplicative metric space, arXiv:1410.3384v2[matn.GN] (2014).
• K. Abodayeh, A. Pitea, W. Shatanawi and T. Abdeljawad, Remarks on multiplicative metric spaces and related fixed point results, arXiv:1512.03771v1[matn.GN] (2015)
• O. Yamaod and W. Sintunavarat, Some fixed point results for generalized contraction mappings with cyclic (α,β)-admissible mapping in multiplicative metric space, Journal of inequalities and applications, 2014:488 (2014).
• X. He, M. Song and D. Chen, Common fixed points for weak commutative mappings on a multiplicative metric space, Fixed point theory and appl., 2014/1/48 (2014).
• S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integerales”, Fundamenta Mathematicae, vol.3 (1922) pp. 133-181.
• R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 60, 1968,71-76.
• Chatterjea, S. K., Fixed point theorems, C.R. Acad. Bulgare Sci. 25,1972, 727-730.
• T. Zamfirescu, Fixed point theorems in metric space. Arch. Math. (Basel), 23,292-298,1972.
• S. Reich, Some remarks concerning contraction mappings, Canadian Mathematical Bulletin 14 (1971) 121–124.
• L. j. B. Ciric, Generalized contractions and fixed point theorems, Publ. Inst.Math. 12 (26)(1971),19-26.
• L. j. B. Ciric, Ageneralization of Banach contraction princible, Proc. Amer. Math. Soc. 45.267-273,1974.
• Hardy, G. E., Rogers, T. D., A generalization of a fixed point theorem of Reich, Canad. Math. Bull., No.2, 201-206,1973.