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Fixed Point Theorems For Set- Valued Mappings in Banach Spaces

Barnita Bharati1 , Kalishankar Tiwary2

Section:Research Paper, Product Type: Journal-Paper
Vol.10 , Issue.3 , pp.57-60, Jun-2023


Online published on Jun 30, 2023


Copyright © Barnita Bharati, Kalishankar Tiwary . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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IEEE Style Citation: Barnita Bharati, Kalishankar Tiwary, “Fixed Point Theorems For Set- Valued Mappings in Banach Spaces,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.3, pp.57-60, 2023.

MLA Style Citation: Barnita Bharati, Kalishankar Tiwary "Fixed Point Theorems For Set- Valued Mappings in Banach Spaces." International Journal of Scientific Research in Mathematical and Statistical Sciences 10.3 (2023): 57-60.

APA Style Citation: Barnita Bharati, Kalishankar Tiwary, (2023). Fixed Point Theorems For Set- Valued Mappings in Banach Spaces. International Journal of Scientific Research in Mathematical and Statistical Sciences, 10(3), 57-60.

BibTex Style Citation:
@article{Bharati_2023,
author = {Barnita Bharati, Kalishankar Tiwary},
title = {Fixed Point Theorems For Set- Valued Mappings in Banach Spaces},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {6 2023},
volume = {10},
Issue = {3},
month = {6},
year = {2023},
issn = {2347-2693},
pages = {57-60},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=3173},
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=3173
TI - Fixed Point Theorems For Set- Valued Mappings in Banach Spaces
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - Barnita Bharati, Kalishankar Tiwary
PY - 2023
DA - 2023/06/30
PB - IJCSE, Indore, INDIA
SP - 57-60
IS - 3
VL - 10
SN - 2347-2693
ER -

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Abstract :
In this paper, we have proved some common fixed point theorems for set-valued mappings which extend some results proved in (Ciric 1965 [4], Pai and Veeramani 1982 [15], Rhoades 1977 [16], and Singh and Tiwary 1992 [18]).

Key-Words / Index Term :
Set-valued mappings, Banach space, Common fixed point, Weakly compact subset, Closed convex subset.

References :
[1] D.E. Anderson, K.L. Singh and J.H.M. Whitfield, Common fixed point in metric space, Jnanabha, 16, 23, 1986.
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[3] F.E. Browder, Non-expansive non-linear operator in a Banach space, Proc. Nat. Acad. Sci., 54, 1041, 1965.
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[8] A.A. Gillespie, B.B. William, Fixed point theorem for a non-expansive mapping of a Banach space with uniformly normal structure, Applicable Analysis, 9, 121, 1979.
[9] A.A. Gillespie, B.B. William, Some theorems on fixed points in Lipschitz and Kannan type mappings, J. Math. Analysis and Application, 74, 382, 1980.
[10] D. Gohde, Zum prinzip der Kontraktivon abbildung, Math. Nach., 30, 1965.
[11] R. Kannan, Construction of fixed points of a class of non-linear mapping, J. Math. Analysis and Application, 41, 2, 430, 1973.
[12] W.A. Kirik, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly, 72, 1004, 1965.
[13] Mainak Mitra, Jigmi Dorjee Bhutia, Kalishankar Tiwary, "On the Existence of Common Fixed Point in a Complete Metric Space Using Integral Type Contraction Conditions," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.6, pp.25-35, 2022.
[14] S B Nadler, Multi Valued Contraction Mappings, Pac. J. Math, 30,475- 488, 1969.
[15] D.V. Pai, P. Veeramani, On some fixed point theorems in Banach spaces, Inter, J. Math. and Math. Sci., 5, 113, 1982.
[16] B.E. Rhoades, Some fixed point theorems in Banach spaces, Math. Sem., Notes, 5, 69, 1977.
[17] Krishnadhan Sarkar, Dinanath Barman, Mithun Paul, Kalishankar Tiwary, "Probabilistic Metric Space, Menger Space and Some Common Fixed Point Theorem," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.5, pp.86-90, 2019
[18] G.N. Singh, Kalishankar Tiwary, Fixed point theorems in Banach Spaces, Bull. Allahabad Math. Soc., 7, 23, 1992.
[19] Kalishankar Tiwary, Biplab Kumar Bag, Chandan Kamelia, "Common Fixed-Point Theorems in Complete Hausdörff Uniform Spaces," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.4, pp.84-88, 2019
[20] Kalishankar Tiwary, Chandan Kamelia, Biplab Kumar Bag, "On Common Fixed Points of Mappings in Hilbert Spaces," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.6, Issue.4, pp.100-103, 2019
[21] Kalishankar Tiwary, S.C. Debnath, Fixed point theorems for set-valued map- pings, Bull. Cal. Math. Soc., 97, (3) 275-282, 2005.

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