Results in strongly minihedral cone and scalar weighted cone metric spaces and applications

Anita Tomar; Meena Joshi

Published: 2021-08-30

Vol. 35 No. 2 (2021)

Results in strongly minihedral cone and scalar weighted cone metric spaces and applications

Anita Tomar

, Meena Joshi

Abstract

The convergence of sequences and non-unique fixed points are established in M-orbitally complete cone metric spaces over the strongly minihedral cone, and scalar weighted cone assuming the cone to be strongly minihedral. Appropriate examples and applications validate the established theory. Further, we provide one more answer to the question of the existence of the contractive condition in Cone metric spaces so that the fixed point is at the point of discontinuity of a map. Also, we provide a negative answer to a natural question of whether the contractive conditions in the obtained results can be replaced by its metric versions.

Keywords:

Cone metric space , strongly minihedral , normal cone , nonunique fixed point

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Tomar, A., & Joshi, M. (2021). Results in strongly minihedral cone and scalar weighted cone metric spaces and applications. Annales Mathematicae Silesianae, 35(2), 302–318. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13455

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References

1. C.D. Aliprantis and R. Tourky, Cones and Duality, Graduate Studies in Mathematics, 84, American Mathematical Society, Providence, 2007.
2. K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985.
3. L.G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), no. 2, 1468–1476.
4. Z. Kadelburg, S. Radenović, and V. Rakočević, Topological vector space-valued cone metric spaces and fixed point theorems, Fixed Point Theory Appl. 2010, Art. ID 170253, 17 pp.
5. L.V. Kantorovich, On some further applications of the Newton approximation method, Vestnik Leningrad. Univ. Ser. Mat. Meh. Astr. 12 (1957), no. 7, 68–103 (in Russian).
6. E. Karapınar, Some nonunique fixed point theorems of Ćirić type on cone metric spaces, Abstr. Appl. Anal. 2010, Art. ID 123094, 14 pp.
7. M.A. Khamsi, Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl. 2010, Art. ID 315398, 7 pp.
8. S.D. Lin, A common fixed point theorem in abstract spaces, Indian J. Pure Appl. Math. 18 (1987), no. 8, 685–690.
9. Sh. Rezapour and R. Hamlbarani, Some notes on the paper “Cone metric spaces and fixed point theorems of contractive mapping”, J. Math. Anal. Appl. 345 (2008), no. 2, 719–724.
10. B.E. Rhoades, Contractive definitions and continuity, in: R.F. Brown (ed.), Fixed Point Theory and Its Applications, Contemp. Math., 72, Amer. Math. Soc., Providence, 1988, pp. 233–245.
11. B. Rzepecki, On fixed point theorems of Maia type, Publ. Inst. Math. (Beograd) (N.S.) 28(42) (1980), 179–186.
12. A. Sonmez and H. Cakalli, Cone normed spaces and weighted means, Math. Comput. Modelling 52 (2010), no. 9-10, 1660–1666.
13. J.S. Vandergraft, Newton’s method for convex operators in partially ordered spaces, SIAM J. Numer. Anal. 4 (1967), 406–432. Google Scholar

Vol. 35 No. 2 (2021)
Published: 2021-09-10

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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