Data dependence results of a new multistep and S-iterative schemes for contractive-like operators

In this paper, we prove that convergence of a new iteration and S-iteration can be used to approximate to the fixed points of contractive-like operators. We also prove some data dependence results of this new iteration and S-iteration schemes for contractive-like operators. Our results extend and improve some known results in the literature.Comment: arXiv admin note: text overlap with arXiv:1211.570

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 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)

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 of Ishikawa iterative sequence for strongly pseudocontractive operators in arbitrary Banach spaces

Under the condition of removing the restriction any bounded, we give the convergence of the Ishikawa iteration process to a unique fixed point of a strongly pseudocontractive operator in arbitrary real Banach space. Furthermore, general convergence rate estimate is given in our results, which extend the recent results of Ciric [3] and Soltuz [12]