### THE COMPARABLY ALMOST (S,T)- STABILITY FOR RANDOM JUNGCK-TYPE ITERATIVE SCHEMES

**DOI Number**

**First page**

**Last page**

#### Abstract

The purpose of this paper is to introduce the concept of generalized - weakly con-

tractive random operators and study a new concept of stability introduced by Kim [15] which is alled comparably almost stability and then prove the comparably almost (S,T)- stability for the Jungck-type random iterative schemes. Our results extend, improve and unify the recent results in [15], [19], [32] and many others. We also give stochastic version of many important known results.

#### Keywords

#### Full Text:

PDF#### References

Y. I. Alber, S. Guerre-Delabriere, Principle of weakly contractive maps in Hilbert spaces. In: Gohberg, I, Lyubich,

Y(eds.) New Results in Operator Theory and Its Applications .Birkhuser, Basel 98 (1997) 7-22.

I. Beg, Approximaton of random xed points in normed spaces, Nonlinear Anal. 51 (2002) 1363-1372.

I. Beg, Minimal displacement of random variables under Lipschitz random maps, Topol. Methods Nonlinear Anal.

(2002) 391-397.

I. Beg, M. Abbas, Iterative procedure for solutions of random operator equations in Banach spaces, J. Math. Appl.

(2006) 181-201.

AL-BAQERI

I. Beg, N. Shahzad, Random xed point theorems for nonepansive and contractive type random operators on

Banach spaces, J. Appl. Math. Stochastic Anal. 7 (1994) 569-580.

A.T. Bharucha-Reid, Fixed point theorems in probabilistic analysis, Bull. Amer. Math. Soc. 82 (1976) 641-657.

O. Hans, Reduzierende zulliallige transformaten, Czechoslovak Math. J. 7 (1957) 154-158.

O. Hans, Random operator equations, Proceedings of the fourth Berkeley Symposium on Math. Statistics and

Probability II (1961) 185-202.

A. M. Harder, Fixed point theory and stability results for xed points iteration procedures, Ph. D. Thesis,

University of Missouri- Rolla, (1987).

A. M. Harder, T. L. Hicks, A stable iteration procedure for nonexpansive mappings, Math. Japonica, 33(5)

(1988) 687-692.

A. M. Harder, T. L. Hicks, Stability results for xed point iteration procedures, Math. Japonica, 33(5) (1988)

-706.

S. Ishikawa, Fixed points by a new iteration method. Proceedings of the American Mathematical Society 44

(1974) 147-150.

S. Itoh, Random xed point theorems with an application to random dierential equations in Banach spaces, J.

Math. Anal. Appl. 67 (1979) 261-273.

G. Jungck. Commuting mappings and xed points. The American Mathematical Monthly. 83 (1976) 261-263.

K. S. Kim, Convergence and stabililty of generalized -weak contraction mapping in CAT(0) Spaces, Open Math.

(2017) 1063-1074.

W. R. Mann, Mean Value methods in iteration. Proceedings of the American Mathematical Society, 4 (1953)

-510.

M. A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl. 251 (2000)

-229.

G. A. Okeke, M. Abbas, Convergence and almost sure T-stability for a random iterative sequence generated by

a generalized random operator, Journal of Inequalities and Applications 146 (2015) 1-11.

G. A. Okeke, J. K. Kim, Convergence and summable almost T-stability of the random Picard-Mann hybrid

iterative process, Journal of Inequalities and Applications 290 (2015).

G. A. Okeke, J. K. Kim, Convergence and (S,T)-stability almost surely for the random Jungck-type iteration

processes with applications, Congent Mathematics 3:1258768 (2016) 1-15.

M. O. Olatinwo, Some stability and strong convergence results for the Jungck-Ishikawa iteration process. Creative

Mathematics and Informatics 17 (2008) 33-42.

M. O. Olatinwo, Some stability results for two hybrid xed point iterative algorithms of Kirk-Ishikawa and

Kirk-Mann type. Journal of Advanced Mathematical Studies 1 (2008) 514.

M. O. Osilike, Stability of the Mann and Ishikawa iteration procedures for - strong pseudo-contractions and

nonlinear equations of the - strongly accretive type. J. Math. Anal. Appl. (1998) 227(2) 319-334.

N. S. Papageorgiou, Random xed point theorems for measurable multifunction in Banach spaces, Proc. Amer.

Math. Soc. 97 (1986) 507-514.

W. Phuengrattana, S. Suantai, On the rate of convergence of Mann, Ishikawa, Noor and SP iterations for

continuous functions on an arbitrary interval, J. Comp. Appl. Math. 235 (2011) 3006-3014.

R. A. Rashwan, H. A. Hammad and G. A. Okeke, Convergence and almost sure (S,T)-stability for random

iterative schemes, International Journal of Advances in Mathematics, 2016 NO.1 (2016) 1-16.

B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal. 47(4) (2001) 2683-2693.

S. L. Singh, C. Bhatnagar and S. N. Mishra, Stability of Jungck-type iterative procedures, International Journal

of Mathematics and Mathematical Sciences 19 (2005) 3035-3043.

A. Spacek, Zufallige gleichungen, Czechoslovak Math. J. 5(1955) 462-466.

H. K. Xu, Some random xed point theorems for condensing and nonexpansive operators, Proc. Amer. Math.

Soc. 110 (1990) 103-123.

Z. Xue, The convergence of xed point for a kind of weak contraction, Nonlinear Func. Anal. Appl. 21(3) (2016)

-500.

SS. Zhang, XR. Wang, M. Liu, Almost sure T-stability and convergence for random iterative algorithms, Appl.

Math. Mech. 32(6) (2011) 805-810.

DOI: https://doi.org/10.22190/FUMI1902175A

### Refbacks

- There are currently no refbacks.

ISSN 0352-9665 (Print)