Fixed point theorems in $S$- metric spaces

L.T. Saji; G. Uthaya Sankar; A. Subramanian

doi:10.26637/MJM0804/0168

Abstract

Sedghi et al. [7,8] introduced $S$-metric space and established some fixed point theorems for a selfmapping on a complete $S$-metric space. In this paper, we prove some fixed point theorems for surjection satisfying various expansive type conditions in the setting of an $S$-metric space.

Keywords:

surjection, expansive mapping, fixed point, $S$-metric spaces

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

L.T. Saji Department of Mathematics, The M.D.T.Hindu College, Tirunelveli, India-627010.
G. Uthaya Sankar Department of Mathematics, Manonmaniam Sundaranar University College, Sankarankoil, India-627756. 3Department of Mathematics, The M.D.T.Hindu College, Tirunelveli, India-627010
A. Subramanian Department of Mathematics, The M.D.T.Hindu College, Tirunelveli, India-627010. Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli-627012.

Pages: 2296-2298
Date Published: 01-10-2020
Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)

Aage, C.T., Salunke, J.N.: Some fixed point theorems for expansion onto mappings on cone metric spaces, Acta Math. Sin. Engl. Ser. 27(6), (2011) 1101-1106. DOI: https://doi.org/10.1007/s10114-011-9606-9

Daffer, P. Z., Kaneko, H.: On expansive mappings, Math. Japonica. 37, 1992 733-735.

Daheriya, R. D., Jain, R., Ughade, M.: Some Fixed Point Theorem for Expansive Type Mapping in Dislocated Metric Space, ISRN Mathematical Analysis, 2(3)(2012) 11 18. DOI: https://doi.org/10.5402/2012/376832

Dhage, B.C.: A study of some fixed point theorem, Ph.D. thesis, Marathwada University, Aurangabad, India (1984).

Mustafa, Z., Sims, B.: A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7(2), (2006) 289-297.

Mustafa, Z., Sims, B.: Some results concerning D-metric spaces., In: Proceedings of the International Conferences on Fixed Point Theory and Applications, Valencia, Spain, (2003) 189-198.

Sedghi, S., Dung, N. V.: Fixed point theorems on S-metric spaces, Mat. Vesnik 66, (2014) 113-124. DOI: https://doi.org/10.1186/1687-1812-2014-43

Sedghi, S., Shobe, N., Aliouche, A., : A generalization of fixed point theorem in S-metric spaces, Mat. Vesnik 64, (2012) 258 -266.

Sharma, AK : A note on fixed points in 2-metric spaces, Indian J. Pure Appl. Math. 11(2) (1980) 1580-1583.

Shatanawi, W., Awawdeh, F. : Some fixed and coincidence point theorems for expansive maps in cone metric spaces, Fixed Point Theory and Applications 3(2) 2012, 20122019. DOI: https://doi.org/10.1186/1687-1812-2012-19

Wang, S. Z., Li, B. Y., Gao, Z. M., Iseki, K.,: Some fixed point theorems for expansion mappings, Math. Japonica. 29, (1984) 631-636.

Xianjiu Huang, Chuanxi Zhu, Xi Wen,: Fixed point theorems for expanding mappings in Partial metric spaces, $A n$. St. Univ. Ovidius Constanta 20(1), (2012) 213-224. DOI: https://doi.org/10.2478/v10309-012-0014-7

Yan Han and Shaoyuan Xu,: Some new theorems of expanding mappings without continuity in cone metric spaces, Fixed Point Theory and Applications, 2013, 2013:30. DOI: https://doi.org/10.1186/1687-1812-2013-3