Sentence examples for extended for developing from inspiring English sources

The iterative algorithm [[8], Theorem 5.7] is extended for developing our Mann's type extragradient algorithm in Theorem 3.1.

The iterative algorithm [[7], Theorem 5.7] is extended for developing our relaxed extragradient algorithm with regularization in Theorem 3.1.

Remark 3.4 Theorem 3.1 improves and extends [[7], Theorem 5.7] in the following aspects: (a) The iterative algorithm [[7], Theorem 5.7] is extended for developing our relaxed extragradient algorithm with regularization in Theorem 3.1.

The corresponding iterative algorithms in [15], Theorem 3.6 and [23], Theorem 3.2 are extended for developing our Ishikawa-type extra-gradient iterative algorithm involved in pseudo-contractive mappings with Lipschitz assumption in Theorem 3.1.

The corresponding iterative algorithms in [15], Theorem 3.6 and [23], Theorem 3.2 are extended for developing our Mann-type extra-gradient iterative algorithm involved in pseudo-contractive mappings without Lipschitz assumption in Theorem 4.1.

Then the sequence { x n } converges weakly to an element x ˆ ∈ Fix ( T ) ∩ Γ. Remark 3.4 Theorem 3.1 improves and extends [[8], Theorem 5.7] in the following respects: (a) The iterative algorithm [[8], Theorem 5.7] is extended for developing our Mann's type extragradient algorithm in Theorem 3.1.

Section 2 formulates a triangulation problem according to available literature and extends it for developing a new method to compare two or more IOTs.

The goal of the documentation effort described is to capture the experience of creating experiential futures and extend the capacity for developing social foresight through a participatory exhibit and online social platform.

The main contributions of this work can be summarized in the following: (a) designing of novel vector-based morphological operators that can be used with color images and (b) the designed operators were extended to be implemented for developing vector-based tools for noise suppression, texture analysis, shape analysis, edge detection and skeletonization.

They were guided by two supervisors from the Central Norway Regional Health Authority who had extended experience in coaching for developing clinical pathways within hospitals.

The UKPDS and FHS risk estimates suggested that favorable developments in the risk for developing CHD extended to all three major racial or ethnic groups.