Random quadruple coincidence points theorems for sequence of random mappings and application

Volume 9, Issue 3, pp 977--988 http://dx.doi.org/10.22436/jnsa.009.03.26

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Authors

Xiaofang Yan - Department of Mathematics, Nanchang University, Nanchang, 330031, P. R. China. Chuanxi Zhu - Department of Mathematics, Nanchang University, Nanchang, 330031, P. R. China. Zhaoqi Wu - Department of Mathematics, Nanchang University, Nanchang, 330031, P. R. China.

Abstract

In this paper, we give the definitions of compatibility and weakly reciprocally continuity for sequence of random mappings \(T_i\) and a random self-mapping g. Further, using these definitions we establish quadruple random coincidence and quadruple random fixed point results by applying the concept of an \(\alpha\)-series for sequence of mappings, introduced by Sihag et al. [V. Sihag, R. K. Vats, C. Vetro, Quaest. Math., 37 (2014), 1-6], in the setting of partially ordered metric spaces. Our results are some random versions and extensions of results relating to triple fixed points theorems by R. K. Vats et al. [R. K. Vats, K. Tas, V. Sihag, A. Kumar, J. Inequal. Appl., 2014 (2014), 12 pages], we also give some examples to illustrate our results.

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Keywords

• Random quadruple coincidence point
• quadruple random fixed point
• \(\alpha\)-series
• partially ordered metric space.

MSC

•  47H10
•  60H25

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