Abstract—It is proved that Kuhfittig iteration pro- cess converges to a **common** **fixed** **point** **of** a **finite** **family** **of** **quasi**-**nonexpansive** **maps** on a Banach space. This result is extended to the random case. Our work improves upon several well-known results in the cur- rent literature.

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Abstract. In this paper, we give some necessary and sufficient conditions for an implicit it- eration process with errors for a **finite** **family** **of** asymptotically **quasi**-**nonexpansive** mappings converging to a **common** **fixed** **of** the mappings in convex metric spaces. Our results extend and improve some recent results **of** Sun, Wittmann, Xu and Ori, and Zhou and Chang.

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and Noor [6] studied some necessary conditions for three- step iterative sequences **of** asymptotically **nonexpansive** mappings to converge to **fixed** points. Cho, Zhou and Guo [7] researched some necessary conditions for three-step iterative sequences with errors **of** asymptotically nonex- pansive mappings to converge to **fixed** points. Quan et. al. [8] studied the weak and strong convergence **of** **finite** steps iterative sequences with mean errors to a **common** **fixed** **point** for a **finite** **family** **of** asymptotically nonex- pansive mappings.

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Very recently, Saeidi [9] introduced a more general iterative algorithm for finding a **common** element **of** the set **of** solutions for a system **of** equilibrium problems and **of** the set **of** **common** **fixed** points for a **finite** **family** **of** **nonexpansive** mappings and a **nonexpansive** semigroup.

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Moreover, increase in refinement **of** aluminium structure results from influence **of** rotate electromagnetic field on liquid metal in time **of** its solidification in mould. However in this case effectiveness **of** inoculation fundamentally depends on value **of** frequency **of** supply voltage feeding induction coil, which generates electromagnetic field. Application **of** frequency **of** supply voltage f 50 Hz does not guarantee favourable transformation **of** pure aluminium structure. Whereas induction coil fed with frequency **of** supply voltage larger than power network i.e. 75 Hz or mainly 100 Hz, generates rotate electromagnetic field, which guarantees favourable refinement **of** structure from **point** **of** view **of** assumed criterion **of** minimum value **of** factor R (Tab. 2 and Fig. 6c). In this case value **of** factor R is more favourable in comparison with value obtained for aluminium after Ti and B inoculation and after **common** influence **of** both modifying factors.

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Cast alloys used for high-duty parts operating in automotive industry and aviation should, besides excellent mechanical properties, offer also stable and failure-free performance. A good measure **of** the reliability **of** a selected examined property, e.g. the tensile strength Rm, is estimation **of** the value **of** Weibull modulus, closely related with the, so called, part’s survival probability [1].

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The paper presents a statistical assessment **of** the effect **of** chemical composition on mechanical properties **of** hypereutectic AlSi17 silumin, which is expected to act as a counterpart **of** alloys used by automotive industry and aviation for casting **of** high-duty engine parts in West European countries and USA. The studies on the choice **of** chemical composition **of** silumins were preceded by analysis **of** the reference literature to state what effect some selected alloying elements and manufacturing technology may have on the mechanical properties (HB, R m and A 5 ) **of** these alloys. As alloying additives, Cu, Ni and Mg in proper combinations were used. The alloy after

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This work in combination with industrial tests **of** casting welding show that the causes **of** high-temperature brittleness are the partial tears **of** the structure and the hot cracks **of** both the castings and the welded and padded joints. Such phenomena should be treated as irreversible failures caused by the process **of** crystallisation that is in the area **of** co-existence **of** the solid and liquid structural constituent. The assessment **of** the resistance to hot fractures was conducted on the basis **of** the transvarestriant trial. The transvarestriant trial consists in changing **of** strain during welding It was stated that the range **of** the high-temperature brittleness is very broad, which significantly limits the application **of** the welding techniques to join or mend the elements made **of** alloy ZRE-1. The brittleness is caused mainly by metallurgical factors, i.e., precipitation **of** inter-metal phases from the solid solution.

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Richardson with SOR, Chebyshev with Gauss-Seidel and Chebyshev with SOR. The iterative schemes were applied to Banded system, Tridiagonal systems and SPD system with varying dimensions. The Krylov subspace methods: GMRES, QMR, MINRES and BiCGSTAB converged to an approximate solutions less than or equal to the dimension **of** the coefficient matrix for each identified systems **of** linear equations. Again, Chebyshev and Richardson acceleration methods were the fastest convergence methods in terms **of** number **of** **iterations**. Again, Residual smoothing and the accelerated gradient schemes should be used for large and sparse systems **of** linear equations. The acceleration processes were very efficient when solving large and sparse systems **of** linear equation and therefore useful especially for systems resulting from the solution **of** partial differential equations.

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Our general idea relies on the assumption that **family** planning interventions have a first-order effect on fertility decisions. There is a bulk **of** evidence supporting this. See May (2012) and Schultz (2008), among many others. For instance, Bloom, Canning, Fink, and Finlay (2009) show that removing legal restrictions on abortion significantly reduces fertility and that this has a positive impact on female labor force participation. Joshi and Schultz (2013) study the long-run consequences **of** a randomized control trial **of** contra- ception provision in Matlab, Bangladesh. Their findings suggest that treatment villages experienced a decline in fertility **of** about 17 percent compared to control villages, and that the effects were persistent over a 20-year period. Sinha (2005) estimates similar effects **of** this **family** planning experiment on fertility. Using an experiment in Zambia, Ashraf, Field, and Lee (2014) show that the local average treatment effect estimation implies that use **of** **family** planning services during about two years **of** the experiment was associated with a 27 percent reduction in births. Using variation in the timing and location **of** the Profamilia program in Colombia, Miller (2010) finds that availability **of** modern contra- ceptives allowed women to postpone their first birth and to have about 5 percent fewer children in their lifetime. 12 Banerjee, Meng, Porzio, and Qian (2014) estimate the effects

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Helly circle graphs (Durán, 2000) form a natural subclass **of** circle graphs. We say that G is a Helly circle graph if there exists a chord model L for G satisfying the Helly property. (A **family** L **of** chords satisfies the Helly property when every subfamily **of** pairwise intersecting chords **of** L has a **common** **point** **of** intersection.) A conjecture by Durán (2000) states that G is a Helly circle graph if and only if G is a circle graph and contains no induced diamonds (a graph formed by four vertices and five edges.)

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In this section, first we introduce the concept **of** G-contractive mapping in Menger probabilistic G-metric space and then its relation with G-contractive map in its dependent G-metric space is studied. This result shows that the existence **of** a convergent subsequence **of** an iterate sequence (**of** a contractive map) implies the existence **of** a **fixed** **point**.

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The concept **of** metric was introduced by Frechet [10] as an e xtension **of** the distance on the real line. Banach contraction principle was given a shape in the context **of** met ric spaces. Later several generalizations **of** Banach contraction principle were obtained. Also many generalizations **of** metric spaces were obtained and Banach contraction principle was extended to such spaces. Some **of** the generalizations **of** Banach contraction principle were a lso e xtended to the generalized versions **of** metric spaces. Czerwik [8] introduced the concept **of** b-metric spaces in 1993. Since then **fixed** **point** results in b-metric spaces were obtained by several authors. Hit zler and Seda [12] introduced the notion **of** dislocated metric spaces , in the year 2000. In dislocated metric spaces the self distance **of** a **point** may be non-zero and this concept has played a very important role in topology and logical progra mming. Severa l authors have studied **fixed** **point** theory extensively, [see 2,6,11,14]. Co mbin ing several generalizations **of** metric spaces Jle li and Sa met [13] obtained a new generalizat ion

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products (Kim & Chung, 2011:40), so it’s important to recognize consumer purchasing behavior. Many companies use marketing strategies by analyzing consumer behavior in order to study the effect on purchase decision (Jalalkamali & Nikbin, 2010:235). The purchase decision is also influenced by the perceived quality which is also an aspect **of** brand value that makes consumers pay for certain products or services (Yaseen et al., 2011:833). It confirms that the consumer purchase decision on products or services is strongly influenced by customer perception **of** quality **of** value brand. Decision making is a way **of** choosing between two or more possible options when a person has a choice between purchasing or not (Schiffman & Kanuk, 2007). In the assessment stages **of** different choices, the consumers classify different brands and the purchase intention is created in his mind. Shareef et al. (2008) revealed purchase decision is a continuous process, which refers to thoughtful, consistent action undertaken to bring about need satisfaction. Choubtarash et al. (2013) confirmed that purchase decision is a person in the mind who is carefully analyzing the features **of** products, trademarks or services and tries, by using logical methods, to choose a choice that can satisfy the recognized need with the least expenses. Consumers perceived organic as a healthier alternative to conventional foods in that they contain more nutrients which enhance personal well-being organic produce is also considered safer and better in taste and more enjoyable than conventional products (Shaharudin et al., 2010:72). Last organic purchasing is defined as purchasing goods and services which have less harmful for environmental and human health (Othman & Rahman, 2014:93). Purchasing decisions can be measured through several dimensions, including recommend, purchase frequency, overall satisfaction and purchase intention (Shareef et al., 2008:101). The measure is not different from the study by Liu et al. (2009:72) which provide specifications for purchasing decisions by some measures, including product selection, brand selection, object selection, purchase opportunity, and purchase quantity. Consumer purchasing decisions on products had relationship with consumer perceptions **of** quality and risk products (Yee et al., 2011:47). Consumer interest in the products can be improved by an increase in the quality **of** products (Kwak & Kang, 2009:85). And previous research has argued that a consumer perception **of** quality has a positive impact on consumer buying behavior (Wang & Tsai, 2014:27). Based on these studies, next hypothesis as follows:

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The unmodified water glass shows inadequate wetting **of** the surface **of** the quartz grains (Fig. 3). Changes **of** contact angle in time are characterised by high values **of** both the initial contact angle θ 0 (about 45 deg.) a nd the equilibrium angle θ r (about 33

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Molten charge cast iron, after being overheated up to 1400°C, was treated with aluminium introduced beneath the metal mirror. The melt was heated again up to 1360- 1380°C, then cerium mischmetal was added, and the roasted ferrosilicon was introduced five minutes later. The quantities **of** cerium mischmetal and ferrosilicon were equal to 0.11% and 1.29% **of** the achieved cast iron mass. Such quantities had been found optimal in the case **of** spheroidization process **of** low-aluminium cast iron containing about 3% Al [14]. Five minutes after the graphitizing modification with ferrosilicon, sand moulds were poured with molten metal directly from the crucible. The specimens were cast in the shape **of** truncated cones, their average diameter (measured halfway along their test parts) being equal to 20 mm.

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The second group comprised Aro orientalis – Carpinetum, Dentario quinquefoliae – Carpinetum, Aceri tatarico – Quercetum roboris, Quercetum robori – petraeae, Genisto tinctoriae – Quercetum petraeae and Acer campestre with Quercus robur communities. This group was characterized by increased frequencies and dominance **of** Quercus sp., lower values for Fagus sp., while the other two tree genera had maximum probabilities **of** occurrence ranging from 40% to 100%. The last cluster included Lathyro venetus – Fagetum *fagetosum and was characterized (distinctively from other plant communities) by Fagus sp. dominance and Quercus sp. low occurrence probability (maximum **of** 20%). Also, the cluster groups the only combination **of** low Quercus sp. probability occurrence with high Carpinus sp. occurrence probability. Both sub-associations **of** Lathyro venetus – Fagetum provides maximum probability **of** occurrence for mushrooms specialized with Fagus genera, as there were, in this study, Lactarius subdulcis and Russula olivacea. Regarding the differentiation between the second and the third clusters, the fungi that had large amplitude probability **of** occurrence were Lactarius quietus, L. subdulcis and Russula olivacea, all having only one tree genera host. This showed that, mushrooms affinity for particular tree genera can prove as an important driver for an entire fungal group. As others authors found, dominant tree species is one **of** the main drivers for shaping fungal communities in temperate forests [GOLDMANN & al. 2015; SHI & al. 2013]. Fungal species having multiple tree hosts, like Russula delica, R. graveolens, R. grisea, R. heterophylla and R. vesca, could be found in more forest types having at least one tree genera host in its composition. Because **of** that, at regional scales, some mushrooms can be found in many ecosystem types, from Mediterranean [ANGELINI & al. 2015; AZUL & al. 2011] to temperate forests [BUÉE & al. 2011], as shown for ECM species like Russula cyanoxantha or R. delica.

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injective orientation preserving partial transformations on a chain with n elements. A natural question then arose: what happens when we compute the Abelian kernel **of** the Abelian kernel and so on? This was a strong motivation for the present paper since, as the Abelian kernel **of** a **finite** group G coincides with the derived subgroup **of** G, we can use **iterations** **of** the Abelian kernel to define solvable monoids, just as we use **iterations** **of** the derived group to define solvable groups. Let us observe that there are other properties **of** groups, for example, being poly-cyclic, which have attracted the attention **of** many researchers and could be object **of** the same kind **of** generalisation, but we will not explore these in the present paper.

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R.I.C’s. In this case, we can apply the same criteria explained for the standard map. But as there are 2 parameters, we do not obtain a critical value, we obtain a critical set in the (γ , α) plane. Another important application **of** this theory is to obtain properties about the structure **of** the unstable set **of** the above mentioned homoclinic loop (to the saddle-center equilibrium), when the former is unstable. The periodic orbits given by theorem (1) were analyzed in (Addas-Zanata and Grotta Ragazzo 2001) and it was proved that for every vertical rotation number m n > 0, there is an open set in the parameter space with a m n -periodic orbit which is topologically a sink. In particular, it can be proved that, for a **fixed** value **of** γ > 0, given an ǫ > α cr (γ ) > 1, where α cr (γ )

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Although the study **of** the skew product **maps** appear as a modulation **of** heterodimensional cycles, their study is important by itself. The role **of** the skew products is similar to the one **of** the shift for the study **of** the horseshoe. As in heterodimensional cycles, the fiber dynamics are given by a system F t **of** iterated functions. In fact, this is an important tool **of** this work.

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