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## Dendrite-type attractors of infinite iterated function systems

### Afrika Matematika (2015-09-01) 26: 1161-1169 , September 01, 2015

The aim of this paper is to establish a necessary and sufficient condition for the attractor of an infinite iterated function system to be a dendrite. In that sense, we will consider the associated graph of an attractor and prove that, in some conditions, the attractor is a dendrite if and only if the associated graph is an infinite tree.

## Chemically reactive solute transfer in boundary layer flow along a stretching cylinder in porous medium

### Afrika Matematika (2014-03-01) 25: 1-10 , March 01, 2014

This paper presents the distribution of solute undergoing first order chemical reaction in axi-symmetric laminar boundary layer flow towards a stretching cylinder embedded in porous medium. Similarity transformations are used to convert the partial differential equations corresponding to the momentum and concentration equations into highly non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that velocity decreases with increasing permeability parameter. The skin friction as well as the mass transfer rate at the surface is larger for a cylinder compared to a flat plate.

## Weyl semisymmetric submanifolds satisfying Chen’s equality

### Afrika Matematika (2015-06-01) 26: 523-528 , June 01, 2015

The object of the present paper is to study Weyl semisymmetric submanifolds satisfying Chen’s equality in a Euclidean space.

## Iterative methods for convex proximal split feasibility problems and fixed point problems

### Afrika Matematika (2016-06-01) 27: 501-517 , June 01, 2016

In this paper we prove strong convergence result for a problem of finding a point which minimizes a proper convex lower-semicontinuous function *f* which is also a fixed point of a total asymptotically strict pseudocontractive mapping such that its image under a bounded linear operator *A* minimizes another proper convex lower-semicontinuous function *g* in real Hilbert spaces. In our result in this work, our iterative scheme is proposed with a way of selecting the step-size such that its implementation does not need any prior information about the operator norm ||*A*|| because the calculation or at least an estimate of the operator norm ||*A*|| is very difficult, if it is not an impossible task. Our result complements many recent and important results in this direction.

## A note on prime ring with generalized derivation

### Afrika Matematika (2017-06-01) 28: 555-561 , June 01, 2017

Let *R* be a prime ring of characteristic different from two with center *Z*(*R*). In the present paper we study the case when a generalized derivation *F* associated with a nonzero derivation *d* of *R* satisfies
$$[F([x, y]_k), [x, y]_k]\in Z(R)$$
for all *x*, *y* in some appropriate subset of *R*, where *k* is a fixed positive integer. We obtain a description of the structure of *R* and information on the form of *F* in terms of the standard identity
$$s_4$$
and the multiplication by the specific element from the extended centroid.

## Generalizations of basic and large submodules of $$QTAG$$ -modules

### Afrika Matematika (2014-12-01) 25: 975-986 , December 01, 2014

A $$QTAG$$ -module $$M$$ over an associative ring $$R$$ with unity is $$k$$ -projective if $$H_k(M)=0$$ and for a limit ordinal $$\sigma ,$$ it is $$\sigma $$ -projective if there exists a submodule $$N$$ bounded by $$\sigma $$ such that $$M/N$$ is a direct sum of uniserial modules. $$M$$ is totally projective if it is $$\sigma $$ -projective for all limit ordinals $$\sigma .$$ If $$\alpha $$ denotes the class of all $$QTAG$$ -modules $$M$$ such that $$M/H_\beta (M)$$ is totally projective for every ordinal $$\beta <\alpha ,$$ then these modules are called $$\alpha $$ -modules. Here we study these $$\alpha $$ -modules and generalize the concept of basic submodules as $$\alpha $$ -basic submodules. It is found that every $$\alpha $$ -module $$M$$ contains an $$\alpha $$ -basic submodule and any two $$\alpha $$ -basic submodules of $$M$$ are isomorphic. A submodule $$L$$ of an $$\alpha $$ -module is $$\alpha $$ -large if $$M=L+B,$$ for any $$\alpha $$ -basic submodule $$B$$ of $$M.$$ Many other interesting properties of $$\alpha $$ -basic, $$\alpha $$ -large and $$\alpha $$ -modules are studied.

## Backward error analysis of the extended iterative refinement or improvement algorithm for solving ill conditioned linear system

### Afrika Matematika (2015-06-01) 26: 509-521 , June 01, 2015

Solving an ill conditioned linear system $$Ax = b$$ is a central problem in matrix computations. We solved the ill conditioned linear system $$Ax = b$$ using the preconditioning method and the Schur aggregation approach. The Schur aggregation is a process of transforming the linear system $$Ax = b$$ into better conditioned linear systems of small sizes, with well conditioned matrices $$V^HC^{-1}$$ , $$C^{-1}U$$ , and $$S = I_{r} - V^HC^{-1}U$$ using the Sherman–Morrison–Woodbury formula $$A^{-1}=(C-UV^H)^{-1}=C^{-1}+C^{-1}U(I_r-V^HC^{-1}U)^{-1}V^HC^{-1}$$ . We used the technique of extended iterative refinement or improvement algorithm to compute the Schur aggregate $$S = I_{r} - V^HC^{-1}U$$ with high precision. In this paper we provide an extensive backward error analysis of the algorithm also we calculate a bound of the backward error.

## Fundamental and plane wave solution in swelling porous medium

### Afrika Matematika (2014-06-01) 25: 397-410 , June 01, 2014

In the present paper propagation of plane waves in swelling porous medium (SP) is studied. The phase velocity and attenuation coefficients of these waves are computed numerically and presented graphically. The results so obtained have been compared to without swelling porous elastic medium (EL). The fundamental solution of the system of differential equations in swelling porous medium in case of steady oscillations in terms of elementary functions has been constructed. Some basic properties are established and particular case of interest is also deduced.

## Common fixed point theorems under generalized $$\mathcal {W}$$ W -weakly contractive condition in ordered orbitally complete metric spaces

### Afrika Matematika (2016-03-01) 27: 297-312 , March 01, 2016

We propose common fixed point results for two pairs of partially weakly increasing mappings in an ordered orbitally complete metric space under a generalized rational-type $$\mathcal {W}$$ -weakly contractive condition. As an application, an existence result for certain systems of integral equations is presented.

## $$\mathcal{I }$$ -statistical convergence of a sequence of random variables in probability

### Afrika Matematika (2014-09-01) 25: 681-692 , September 01, 2014

In this paper we make a new approach to some well known summability methods using ideals and introducing new notions like $$\mathcal{I }$$ -statistical convergence of a sequence of random variables in probability, $$\mathcal{I }$$ -lacunary statistical convergence of a sequence of random variables in probability and $$\mathcal{I }$$ - $$\lambda $$ -statistical convergence of a sequence of random variables in probability. Further we investigate their interrelationship and study some of their important properties.