Fixed point theorems for self-maps on 4-dimensional ball metric spaces and extension to n-dimensional (n≥4) ball metric spaces

Ravi

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Fixed point theorems for self-maps on 4-dimensional ball metric spaces and extension to n-dimensional (n≥4) ball metric spaces

Ravi KumarSsangamravi4u@gmail.com ^*

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Abstract

Metric spaces are generalized to three variables and are termed S - metric spaces, which in turn are extended to four variables and are termed B_4 - metric spaces. Now we extend this notion to n - variables (n≥4), which we name as B_n - metric spaces. We study novel contractive mappings on B_n - metric spaces. In this paper, we obtain a fixed point theorem for a self-map on a 4-dimensional ball metric space and also obtain a fixed point theorem for a self-map on an n-dimensional (n≥4) ball metric space and generalize known results in fixed point theorems on metric spaces.

Keywords

B_4 - metric spaces B_n - metric spaces 4-dimensional ball metric spaces n-dimensional (n≥4) ball metric spaces Fixed point theorems.

References

[1] K.K.M. Sarma, Ch. Srinivasa Rao and S. Ravi Kumar.: B4- metric spaces and Contractions, International Journal of Engineering Research and Applications 13(1): (2023), 43-50.

[2] Ch. Srinivasa Rao, S. Ravi Kumar and K.K.M. Sarma.: Contractive mappings on Bn-metric spaces, Eur. Chem. Bull,12(5): 2023, 5399-5412.

[3] Ch. Srinivasa Rao, S. Ravi Kumar and K.K.M. Sarma.: Fixed point theorems on - metric spaces, Eur. Chem. Bull,12(7): 2023, 1020-1039.

[4] Ch. Srinivasa Rao, S. Ravi Kumar and K.K.M. Sarma B4- metric spaces and Fixed point theorems, Submitted for publication.

[5] O.K. Adewale and C. Iluno.: Fixed point theorems on rectangular S- metric spaces, Scientific African 16: (2022) e01202.

[6] S. Sedghi, N. Shobe, A. Aliouche.: A generalization of Fixed point theorem in S -metric spaces, Mat. Vesn. 64: (2012) 258-266.

[7] Ciric B. Lj. A generalization of Banach's contraction principle.: Proc. Am. Math. Soc. 45(2): (1974), 267-273. [8] Nihal Yilmaz Ozgur, Nihal Tas.: Some generalizations of fixed point theorems on -metric spaces. Essays in Mathematics and Its Applications in Honor of Vladimir Arnold, New York, (2016), Springer.

[9] Nihal Yilmaz Ozgur, Nihal Tas.: Some new contractive mappings on S-metric Spaces and their relationships with the mapping (S25). Springer 11: (2017), 7 -16.

[10] Sedghi, S., Dung, N.V.: Fixed point theorems on -metric spaces. Mat. Vesnik 66(1): (2014), 3-124. [11] Aghajani, A., Abbas, M., Roshan, J.R.: Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces. Math. Slovaca 64 (4): (2014), 940 - 960.

[12] An, T.V., Dung, N.V., Hang, V.T.L.: A new approach to fixed point theorems on G-metric spaces. Topol. Appl. 160(7): (2013), 1486-1493.

[13] Bailey, D.F.: Some Theorems on contractive mappings. J. London Math. Soc. 41: (1996), 101-106.

[14] Chang, S.S., Zhong, Q.C.: On Rhoades' open questions. Proc. Am. Math. Soc. 109(1): (1990), 269-274.

[15] Gupta, A.: Cyclic contraction on S-metric space. Int. J. Anal. Appl. 3(2): (2013), 119-130.

[16] Dung, N.V., Hieu, N.T., Radojevic, S.: Fixed point theorems for monotone maps on partially ordered -metric spaces. Filomat 28(9): (2014), 1885-1898.

[17] Fisher, B.: Quasi-contractions on metric spaces. Proc. Am. Math. Soc. 75(2): (1979), 321-325.

[18] Gupta, V., Deep, R.: Some coupled fixed point theorems in partially ordered -metric spaces. Miskolc Math. Notes 16(1): (2015), 181-194.

[19] Hieu, N.T., Ly, N.T., Dung, N.V.: A Generalization of Ciric Quasi Contractions for Maps on S-Metric Spaces. Thai J. Math. 13(2): (2015), 369380.

[20] Rhoades, B.E.: A Comparison of various definitions of contractive mappings. Trans. Am. Math. Soc. 226: (1977), 257-290.

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KumarSsangamravi4u@gmail.com, Ravi. "Fixed point theorems for self-maps on 4-dimensional ball metric spaces and extension to n-dimensional (n≥4) ball metric spaces." International Journal of Neutrosophic Science, vol. , no. , , pp. . DOI:

KumarSsangamravi4u@gmail.com, R. (). Fixed point theorems for self-maps on 4-dimensional ball metric spaces and extension to n-dimensional (n≥4) ball metric spaces. International Journal of Neutrosophic Science, (), . DOI:

KumarSsangamravi4u@gmail.com, Ravi. "Fixed point theorems for self-maps on 4-dimensional ball metric spaces and extension to n-dimensional (n≥4) ball metric spaces." International Journal of Neutrosophic Science , no. (): . DOI:

KumarSsangamravi4u@gmail.com, R. () 'Fixed point theorems for self-maps on 4-dimensional ball metric spaces and extension to n-dimensional (n≥4) ball metric spaces', International Journal of Neutrosophic Science, (), pp. . DOI:

KumarSsangamravi4u@gmail.com R. Fixed point theorems for self-maps on 4-dimensional ball metric spaces and extension to n-dimensional (n≥4) ball metric spaces. International Journal of Neutrosophic Science. ;():. DOI:

R. KumarSsangamravi4u@gmail.com, "Fixed point theorems for self-maps on 4-dimensional ball metric spaces and extension to n-dimensional (n≥4) ball metric spaces," International Journal of Neutrosophic Science, vol. , no. , pp. , . DOI:

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