Stochastic Fixed Point Theorems in Rectangular Metric Spaces

Parveen Kumar¹, Savita Malik^{1, 2,} and Manoj Kumar²

¹Department of Mathematics, Tau Devi Lal Govt. College for Women, Murthal Sonipat-131027, Haryana (India)

²Department of Mathematics, Baba Mastnath University, Asthal Bohar Rohtak-124021, Haryana (India)

Cite this paper:
Parveen Kumar, Savita Malik and Manoj Kumar. Stochastic Fixed Point Theorems in Rectangular Metric Spaces. Turkish Journal of Analysis and Number Theory. 2021; 9(1):9-16. doi: 10.12691/tjant-9-1-2

Abstract

In this paper, we present the random (Stochastic) version of Banach contraction principle and some of its generalizations in setting of rectangular metric spaces.

Keywords:
rectangular metric spaces random fixed point Banach contraction principle

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	Joshi M.C., Bose R.K., Some Topics in Nonlinear Functional Analysis. Wiley Eastern, New Delhi, 1985.
[2]	Okeke G.A., Abbas, M,. Convergence and almost sure T-stability for a random iterative sequence generated by a generalized random operator. J. Inequal. Appl. 146, 1-11, 2015.
[3]	Bharucha-Reid A.T., Random Integral Equations, Academic Press, New York, 1972.
[4]	Binayak Choudhary S., A common unique fixed point theorem for two random operators in Hilbert space, IJMMS, 32(3), 177-182, 2002.
[5]	Rhoades B.E., Iteration to obtain random solutions and fixed points of operators in uniformly convex Banach spaces, Soochow Journal of Mathematics, 27(4), 401-404, 2001.
[6]	Branciari A., “A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces,” Publicationes Mathematicae Debrecen, 57(1-2), 31-37, 2000.
[7]	Azam A., and Arshad M., “Kannan fixed point theorem on generalized metric spaces,” Journal of Nonlinear Sciences and Its Applications, 1(1), 45-48, 2008.
[8]	Chen C. M., and Chen C. H., “Periodic points for the weak contraction mappings in complete generalized metric spaces,” Fixed Point Theory and Applications, 79, 2012.
[9]	Das P., and Dey L. K., “A fixed point theorem in a generalized metric space,” Soochow Journal of Mathematics, 33(1), 33-39, 2007.
[10]	Das P., and Dey L. K., “Fixed point of contractive mappings in generalized metric spaces,” Mathematica Slovaca, 59(4), 499-504, 2009.
[11]	Erhan I. M., Karapinar E., and Sekulic T., “Fixed points of (𝜓−𝜙) contractions on rectangular metric spaces,” Fixed Point Theory and Applications, 138, 2012.
[12]	Karapinar E., “Weak 𝜙-contraction on partial metric spaces and existence of fixed points in partially ordered sets,” Mathematica Aeterna, 1(3-4), 237-244, 2011.
[13]	Lakzian H., and Samet B., “Fixed points for (𝜓 − 𝜙)-weakly contractive mappings in generalized metric spaces,” Applied Mathematics Letters, 25(5), 902906, 2012.
[14]	George R., Radenovi_c S., Reshma K. P., and Shukla S., Rectangular b-metric space and contraction principles, J. Nonlinear Sci. Appl. 8, 1005-1013, 2015.