Fixed point theorems for some mappings in 2-Banach spaces

Ettayb, Jawad

doi:10.30495/maca.2025.2063639.1140

Fixed point theorems for some mappings in 2-Banach spaces

10.30495/maca.2025.2063639.1140

Volume 7, Issue 3
Summer 2025

Pages 67-75

Mathematical Analysis and its Contemporary Applications

Document Type : Original Article

Author

Jawad Ettayb

C. H. School of Hauman El Fetouaki, Had Soualem, Morocco

Abstract

In the present study, we introduce the notions of Meir-Keeler contraction mappings and Ciri´c contraction mappings on nonempty, closed and bounded subsets containing at least two linearly independent vectors of a 2-Banach space. In particular, we discuss the existence and uniqueness of a fixed point of such mappings in nonempty, closed and bounded subsets containing at least two linearly independent vectors of a 2-Banach space. On the other hand, we define the concept of Hardy-Rogers contraction mappings on nonempty, closed and bounded subsets containing at least two linearly independent vectors of a 2-Banach space. In particular, we prove the existence and uniqueness of a fixed point of such a mapping in nonempty, closed and bounded subsets containing at least two linearly independent vectors of a 2-Banach space. However, many results have been proved using fixed point theorems of certain mappings in 2-Banach spaces.

Keywords

Fixed point theorems

2-Banach spaces

closed and bounded sets

[1] R. W. Freese and Y. J. Cho, Geometry of Linear 2-Normed Spaces, Nova Publishers, Inc., New York, 2001.

[2] S. Gähler, Lineare 2-Normierte Räume, Math. Nachr., 28 (1964), 1–43.

[3] S. Gähler, 2-metrische Räume und ihre topologische Struktur, Nath. Nachr., 26 (1963), 115–122.

[4] G. E. Hardy and T. D. Rogers, A generalization of a fixed point theorem of Reich, Canad. Math. Bull., 16(2) (1973), 201–206.

[5] P. K. Harikrishnan and K. T. Ravindran, Some properties of accretive operators in Linear 2-normed spaces, Int. Math. Forum, 6(59) (2011), 2941–2947.

[6] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 60 (1968), 71–76.

[7] M. Kir and H. Kiziltunc, Some New Fixed Point Theorems in 2-Normed Spaces, Int. J. Math. Anal., 58(7) (2013), 2885–2890.

[8] A. Meir and E. Keeler, A theorem on contractive mappings, J. Math. Anal. Appl., 28 (1969), 26–29.

[9] S. Reich, Kannan’s fixed point theorem, Bull. Univ. Mat. Ital., 4 (1971), 1–11.

[10] A. White, 2-Banach spaces, Math. Nachr., 42 (1969), 43–60.

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