• The Pure and Applied Mathematics
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• v.11 no.4
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• pp.337-348
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• 2004

In this paper, we suggest and analyze Noor (three-step) iterative scheme for solving nonlinear strongly accretive operator equation Tχ = f. The results obtained in this paper represent an extension as well as refinement of previous known results.

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.211-217
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• 2006

In this paper, we have shown that the convergence of one-step, two-step and three-step iterations is equivalent, which are known as Mann, Ishikawa and Noor iteration procedures, for a special class of Lipschitzian operators defined in a closed, convex subset of an arbitrary Banach space.

• The Pure and Applied Mathematics
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• v.13 no.1 s.31
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• pp.39-46
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• 2006

We establish a general theorem to approximate fixed points of quasicontractive operators on a normed space through the Noor iteration process with errors in the sense of Liu [9]. Our result generalizes and improves upon, among others, the corresponding result of Berinde [1].

• Honam Mathematical Journal
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• v.39 no.1
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• pp.1-25
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• 2017

In this paper, we introduce a new scheme namely: CUIA-iterative scheme and utilize the same to prove a strong convergence theorem for quasi contractive mappings in Banach spaces. We also establish the equivalence of our new iterative scheme with various iterative schemes namely: Picard, Mann, Ishikawa, Agarwal et al., Noor, SP, CR etc for quasi contractive mappings besides carrying out a comparative study of rate of convergences of involve iterative schemes. The present new iterative scheme converges faster than above mentioned iterative schemes whose detailed comparison carried out with the help of different tables and graphs prepared with the help of MATLAB.

• East Asian mathematical journal
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• v.31 no.3
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• pp.301-310
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• 2015

In this paper, we establish a strong convergence for the Noor iterative scheme associated with Lipschitz strongly pseudocontractive mappings in real Banach spaces. It's proof-method is very simple by comparing with the previous proofs known.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.493-506
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• 2007

In this paper weak and strong convergence theorems of modified Noor iterations to fixed points for asymptotically nonexpansive mappings in the intermediate sense in Banach spaces are established. In one theorem where we establish strong convergence we assume an additional property of the operator whereas in another theorem where we establish weak convergence assume an additional property of the space.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.525-536
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• 2007

In this paper, we prove the weak and strong convergence of the Noor iterative scheme to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize some previous results.

• The Pure and Applied Mathematics
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• v.22 no.2
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• pp.185-197
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• 2015

The author considers a Noor-type iterative scheme to approximate com- mon fixed points of an infinite family of uniformly quasi-sup(f_n)-Lipschitzian map- pings and an infinite family of g_n-expansive mappings in convex cone metric spaces. His results generalize, improve and unify some corresponding results in convex met- ric spaces [1, 3, 9, 16, 18, 19] and convex cone metric spaces [8].

• International Journal of Computer Science & Network Security
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• v.21 no.1
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• pp.34-39
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• 2021

Collaborative ontology construction is the latest trend in developing ontologies. In this technique domain specialists and ontologists need to work together. Because of the complexity associated with ontology construction, it's done in an iterative and incremental fashion. After each iteration, an ontology increment will be produced. Current ontology increment is always an enhanced version of the previous increment. Each ontology increment has to be verified for its accuracy. Domain specialists' contribution is very significant in accomplishing this necessity. Unfortunately, non-computing domain specialists (i.e. medical doctors, bankers, lawyers) are illiterate on semantic concepts. Therefore, validating the accuracy of the ontology increment is a complex hurdle for them. This research proposes verbalization approach to address this complexity.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.557-566
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• 2009

In this paper, we present the three-step mean value iterative scheme and prove that the iteration sequence converge strongly to a common element of the set of fixed points of a nonexpansive mappings and the set of the solutions of the variational inclusions under some mild conditions. The results presented in this paper extend, generalize and improve the results of Noor and Huang and some others.