Weakly Picard mappings

summary:In this paper we generalize the well known converse to the contraction principle due to C. Bessaga, dropping the uniqueness of the fixed point from its hypotheses. Some properties of weakly Picard mappings are given

Available online at www.tjnsa.com J. Nonlinear Sci. Appl. 6 (2013), 97–107 Research Article

schemes of fixed points for multivalued operator

Iterates of a class of discrete linear operators via contraction principle

summary:In this paper we are concerned with a general class of positive linear operators of discrete type. Based on the results of the weakly Picard operators theory our aim is to study the convergence of the iterates of the defined operators and some approximation properties of our class as well. Some special cases in connection with binomial type operators are also revealed

A general functional inequality and its applications

Not available

Quantitative characterisation of extended-release tablets with quetiapine using NIR-chemometric methods

This study aims to develop and validate NIR-chemometric methods for quantifying the API (quetiapine) and two excipients in extended-release tablets without sample preparation. The calibration samples were prepared following an experimental design with three variables (quetiapine, HPMC and microcrystalline cellulose) and five levels (concentration 80-90-100-110-120% of API). The validation set included three concentration levels (90-100-110%). The best calibration algorithms have used the same pre-treatment method (SNV), and different factors: 7 PLS factors (R² -0,966 and RMSEP-6,84) for quetiapine, 8 PLS factors (R²-0,927 and RMSEP 6,84) for HPMC and 3 PLS factors (R²-0,983 and RMSEP-7,26) for microcrystalline cellulose. The methods were fully validated according to the ICH guidance using these calibration models. Regarding the trueness of the methods, the recovery was between 98.51 and 99.43 for quetiapine, between 98.61 and 100.85 for HPMC, and between 100.61 and 101.78 for microcrystalline cellulose. According to data obtained, the accuracy profile was ± 5 for quetiapine and HPMC, and ± 6 for microcrystalline cellulose. Linearity profile was also in establish intervals at accuracy and the R2 value was 0.983 for quetiapine, 0.948 for HPMC and 0.997 for microcrystalline cellulose. In conclusion, the developed NIR-chemometric methods have suitable reproducibility, accuracy, linearity and can be used for quantitative characterisation of extended-release tablets with quetiapine, with any sample preparation

Some problems in the fixed point theory

n this paper we present some of my favorite problems, all the time open, in the fixed point theory. These problems are in connection with the following two: Which properties have the fixed point equations for which an iterative algorithm is convergent ? Let us have a fixed point theorem, T, and an operator f (single or multivalued) which does not satisfy the conditions in T. In which conditions the operator f has an invariant subset Y such that the restriction of f to Y , f|Y , satisfies the conditions of T

Relevant Classes of Weakly Picard Operators

In this paper we consider the following problems