A-contraction mappings of integral type in n-normed spaces
DOI:
https://doi.org/10.23851/mjs.v31i4.889Keywords:
n- Normed spaces, Picard iteration sequence, contractive condition, integral mapping.Abstract
In this article, A-contraction type mappings in integral case are defined on a complete n-normed spaces and the existence of some fixed point theorems are proved in the complete n-normed spaces and given some results on Picard operator.
References
S. Gahler, Lineare 2-Normierte Raume, Math. Nachr., MR 29#6276. Zbl 142.398, 28(1964), 1-43.
S. M. Gozali, H. Gunawan, and O. Neswan, On n-Norms and n-Bounded Linear Functionals in a Hilbert Space, Ann. Funct. Anal., 1 (2010), 72-79.
Z. Lewandowska, Bounded 2-Linear Operators on 2- Normed Sets, Glas. Math. Ser. III, 39(2004), 301-312.
R. Malcheski, and Z. Cvetkovski, Dual Space of the Space of Bounded Linear n-functionals, Math. Bilten, 36(2012), 47-53.
Y. E. P. Pangalela, and H. Gunawan, The n-Dual space of the space of p-summable sequences, Math. Bohem., 138(2013), 439-448.
A. L. Soenjaya, On n-Bounded and n-Continuous Operator in n-Normed Space, J. Indones. Math. Soc., Vol. 18(2012), no. 1, pp. 45-56.
A. White, 2-Banach spaces, Math. Nachr., 42(1969), 43-60.
A. Misiak, n-Inner Product Spaces, Math. Nachr., 140(1989), 299-319.
H. Dutta, and H. Mazaheri, On Some n-normed Sequence Spaces, Math. Sci. Springer Open Journal, (2012).
H. Gunawan, and M. Mashadi, On n-Normed Spaces, IJMMS27:10 (2001), PP. 631-639.
E. Sukaesih, H. Gunawan, O. Neswan, Fixed Point Theorems on Bounded Sets in an n-Normed Space, J. Math. Anal., 3(2015), 51-58.
H. S. Lazam, S. S. Abed, Some Fixed Point Theorems in ???Normed Spaces, Al-Qadi.: J. Pur. Scie., 25 (3) (2020), 1-15.
K. Matsuzaki, Uniform convexity Normal Structure and The Fixed Point Property of Metric Spaces, Top. and its Appl., 196 (2015), pp.684-695.
J. Meng, M. Song, Fixed Point Theorems in Normal n-Normed Spaces, J. Math. Comput. Sci., 7(1)(2017), 84-91.
B. E. Rhoades, Some Theorems on Weakly Contractive Maps,J. Nonli. Anal., 47(2001), 2683-2693.
N. Shahzad, A. F. R. L. Hierro, and F. Khojasteh, Some Fixed Point Theorems under (A, S)-Contractivity Conditions, Racsam, 111(2)(2017), 307-324.
N. S. Taresh, and S.S. Abed, On Stability of Iterative Sequences with Error, Math., 7(765) (2019), 1-11.
X. Wu, Fixed Point Problems for Nonexpansive Mappings in Bounded Sets of Banach Spaces, Adva. Math. l Phys. 2020, Article ID 918, (2016), 1-6.
A. Branciari, A Fixed Point Theorem for Mappings Satisfying a General Contractive Condition of Integral Type, Int. J. Math. Sci., 29(2002), no.9, 531 - 536.
B. E. Rhoades, Two Fixed Point Theorems for Mappings Satisfying a General Contractive Condition of Integral Type, Int. J. of Math. and Math. Sci., 63(2003), 4007 - 4013.
M. Saha, D. Dey, Fixed Point Theorems for A-Contraction Mappings of Integral Type, J. nonlinear sci. Appl., 5(2012), 84-92.
M. Akram, A. A. Zafar, and A. A. Siddiqui, A General Class of Contractions: A- Contractions, Novi. Sad. J. Math., 38(1) (2008), 25-33.
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