Latest News on Contraction Mapping: March -2020

Latest News on Contraction Mapping: March -2020

A random fixed point theorem for a multivalued contraction mapping

Some results on measurability of multivalued mappings are given. Then using them, the following random fixed point theorem is proved; Theorem. Let X be a Polish space, (T,) a measurable space. Let F : T × X → CB(X) be a mapping such that for each x ∈ X, F(⋅,x) is measurable and for each t ∈ T, F(t,⋅) is k(t)-contraction, where k : T → [0,1) is measurable. Then there exists a measurable mapping u : T → X such that for every t ∈ T, u(t) ∈ F(t,u(t)). [1]

Downscaling of remotely sensed soil moisture with a modified fractal interpolation method using contraction mapping and ancillary data

Previous work showed that remotely sensed soil moisture fields exhibit multiscaling and multifractal behavior varying with the scales of observations and hydrometeorological forcing (Remote Sens. Environ. [2]

A contraction mapping preserving balanced reduction scheme and its infinity norm error bounds

A balanced reduction scheme for linear systems, based on the simultaneous diagonalization of the solutions of the dual algebraic Riccatti equations of the bounded real lemma, is introduced. This procedure reduces a bounded stable transfer matrix S(s) (//S///sub infinity /> [3]

A Note on Banach Contraction Mapping principle in Cone Hexagonal Metric Space

In this paper, we prove fixed point theorem of a self mapping in non-normal cone hexagonal metric spaces. Our result extend and improve some recent results of Azam et al., [Banach contraction principle on cone rectangular metric spaces, Applicable Analysis and Discrete Mathematics, 3 (2), 236 – 241, 2009].[4]

Fixed Point Results for Generalized Weakly C- contractive Mappings in Ordered G-partial Metric Spaces

We introduced the class of generalized weakly C-contractive mappings in G-partial metric spaces by combining the characteristics of Hardy and Rogers maps with weak contraction maps. [5]

Reference

[1] Itoh, S., 1977. A random fixed point theorem for a multivalued contraction mapping. Pacific Journal of Mathematics, 68(1), pp.85-90.

[2] Kim, G. and Barros, A.P., 2002. Downscaling of remotely sensed soil moisture with a modified fractal interpolation method using contraction mapping and ancillary data. Remote Sensing of Environment, 83(3), pp.400-413.

[3] Opdenacker, P.C. and Jonckheere, E.A., 1988. A contraction mapping preserving balanced reduction scheme and its infinity norm error bounds. IEEE Transactions on Circuits and Systems, 35(2), pp.184-189.

[4] Auwalu, A. and Hınçal, E. (2016) “A Note on Banach Contraction Mapping principle in Cone Hexagonal Metric Space”, Journal of Advances in Mathematics and Computer Science, 16(1), pp. 1-12. doi: 10.9734/BJMCS/2016/25172.

[5] Eke, K. (2015) “Fixed Point Results for Generalized Weakly C- contractive Mappings in Ordered G-partial Metric Spaces”, Journal of Advances in Mathematics and Computer Science, 12(1), pp. 1-11. doi: 10.9734/BJMCS/2016/18991.

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