2,645 research outputs found
Convergence and summable almost T-stability of the random Picard-Mann hybrid iterative process
The purpose of this paper is to introduce the random Picard-Mann hybrid iterative
process. We establish the strong convergence theorems and summable almost
T-stability of the random Picard-Mann hybrid iterative process and the random
Mann-type iterative process generated by a generalized class of random operators in
separable Banach spaces. Our results are generalizations and improvements of several
well-known deterministic stability results in a stochastic versio
CONVERGENCE AND ALMOST SURE T -STABILITY FOR RANDOM NOOR-TYPE ITERATIVE SCHEME
The purpose of this study is to introduce a Noor-type random iterative scheme
and prove the convergence of this kind of random iterative scheme for certain �-weakly con-
tractive type random operators. The Bochner integrability of random fixed points for this kind
of random operators and the almost sure T -stability and convergence for Noor-type random
iterative scheme are established. Our results are stochastic generalizations of the deterministic
fixed point theorems of Berinde [7, 8] and Rhoades [29]-[32]
Convergence and almost sure T-stability for a random iterative sequence generated by a generalized random operator
The aim of this paper is to introduce the concept of generalized φ-weakly contraction
random operators and then to prove the convergence and almost sure T-stability of
Mann and Ishikawa-type random iterative schemes. We also prove that a random
fixed point of such operators is Bochner integrable. Our results generalize, extend and
improve various results in the existing literature including the results in Berinde (Bul.
¸Stiin¸t. - Univ. Baia Mare, Ser. B Fasc. Mat.-Inform. 18(1):7-14, 2002), Olatinwo (J. Adv.
Math. Stud. 1(1):5-14, 2008), Rhoades (Trans. Am. Math. Soc. 196:161-176, 1974; Indian
J. Pure Appl. Math. 21(1):1-9, 1990; Indian J. Pure Appl. Math. 24(11):691-703, 1993) and
Zhang et al. (Appl. Math. Mech. 32(6):805-810, 201
Convergence and almost sure T-stability for a random iterative sequence generated by a generalized random operator
The aim of this paper is to introduce the concept of generalized φ-weakly contraction
random operators and then to prove the convergence and almost sure T-stability of
Mann and Ishikawa-type random iterative schemes. We also prove that a random
fixed point of such operators is Bochner integrable. Our results generalize, extend and
improve various results in the existing literature including the results in Berinde (Bul.
¸Stiin¸t. - Univ. Baia Mare, Ser. B Fasc. Mat.-Inform. 18(1):7-14, 2002), Olatinwo (J. Adv.
Math. Stud. 1(1):5-14, 2008), Rhoades (Trans. Am. Math. Soc. 196:161-176, 1974; Indian
J. Pure Appl. Math. 21(1):1-9, 1990; Indian J. Pure Appl. Math. 24(11):691-703, 1993) and
Zhang et al. (Appl. Math. Mech. 32(6):805-810, 2011)
Results on a faster iterative scheme for a generalized monotone asymptotically
This article devoted to present results on convergence of Fibonacci-Halpern scheme (shortly, FH) for monotone asymptotically αn-nonexpansive mapping (shortly, ma αn-n mapping) in partial ordered Banach space (shortly, POB space). Which are auxiliary theorem for demi-close's proof of this type of mappings, weakly convergence of increasing FFH-scheme to a fixed point with aid monotony of a norm and  Σn+=∞1 λn= +∞, λn =min{hn , (1-hn)} where hn ⸦ (0,1)  where is associated with FH-scheme for an integer n>0 more than that, convergence amounts to be strong by using Kadec-Klee property and finally, prove that this scheme is weak-w2 stable up on suitable status
A Common Fixed Point Theorem for Two Random Operators using Random Mann Iteration Scheme
Abstract: In this paper, we proved that if a random Mann iteration scheme is defined by two random operators is convergent under some contractive inequality the limit point is a common fixed point of each of two random operators in Banach space. Keywords: Mann iteration, fixed point, measurable mappings, Banach space. AMS Subject Classification: 47H10, 47H40
A Cyclic Douglas-Rachford Iteration Scheme
In this paper we present two Douglas-Rachford inspired iteration schemes
which can be applied directly to N-set convex feasibility problems in Hilbert
space. Our main results are weak convergence of the methods to a point whose
nearest point projections onto each of the N sets coincide. For affine
subspaces, convergence is in norm. Initial results from numerical experiments,
comparing our methods to the classical (product-space) Douglas-Rachford scheme,
are promising.Comment: 22 pages, 7 figures, 4 table
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