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.
Metrics
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.
Downloads
Published
How to Cite
Issue
Section
License
Articles accepted for publication in Al-Mustansiriyah Journal of Science (MJS) are protected under the Creative Commons Attribution 4.0 International License (CC BY-NC). Authors of accepted articles are requested to sign a copyright release form prior to their article being published. All authors must agree to the submission, sign copyright release forms, and agree to be included in any correspondence between MJS and the authors before submitting a work to MJS. For personal or educational use, permission is given without charge to print or create digital copies of all or portions of a MJS article. However, copies must not be produced or distributed for monetary gain. It is necessary to respect the copyright of any parts of this work that are not owned by MJS.