Weak Contraction Research Articles

Molecular theory of the tilting transition in smectic liquid crystals with weak layer contraction and diffused cone orientational distribution

A molecular field theory of the smectic-A-smectic-C transition has been developed for smectics with a diffused cone orientational distribution of molecules (volcano-like distribution function) in the smectic-A phase and anomalously weak layer contraction in the smectic-C phase. Orientational order parameters and smectic layer spacing have been calculated numerically as functions of temperature and compared with the results obtained using a model with a standard Maier-Saupe-type distribution function that has been considered before. A molecular theory of the electroclinic effect in chiral smectics has also been developed using the recently proposed simple biaxial interaction potential. A comparison has been made between the absolute values and temperature variations of the electroclinic coefficient obtained using the volcano model, the model with Maier-Saupe-type distribution, and the orthodox cone model proposed by de Vries. It has been shown that the model with a conventional "sugar loaf" type orientational distribution function in the smectic-A phase is sufficient to describe the main properties of smectics with anomalously weak layer contraction.

Random approximation with weak contraction random operators and a random fixed point theorem for nonexpansive random self-mappings

In real reflexive separable Banach space which admits a weakly sequentially continuous duality mapping, the sufficient and necessary conditions that nonexpansive random self-mapping has a random fixed point are obtained. By introducing a random iteration process with weak contraction random operator, we obtain a convergence theorem of the random iteration process to a random fixed point for nonexpansive random self-mappings.

Common Fixed Points of Weak Contractions in Cone Metric Spaces

Results on common fixed points of mappings in cone metric spaces under weak contractive conditions (B. S. Choudhury and N. Metiya (2010)) are unified and generalized. Also, cone metric versions of some other related results on weak contractions are proved. Examples show that our results are different than the existing ones.

An Extension of Generalized -Weak Contractions

We prove a fixed-point theorem for a class of maps that satisfy generalized -weak contractions depending on a given function. An example is given to illustrate our extensions.

Common fixed point of generalized ($psi$-$varphi$)-weak contraction mappings

Let (X; d) be a complete metric space and let f; g : X 􀀀! X betwo mappings which satisfy a ( 􀀀 ')-weak contraction condition or generalized( 􀀀 ')-weak contraction condition. Then f and g have a unique common xedpoint. Our results extend previous results given by Ciric (1971), Rhoades (2001),Branciari (2002), Rhoades (2003), Abbas and Ali Khan (2009), Zhang and Song(2009) and Moradi at. el. (2011).

A COMMON FIXED POINT RESULT FOR A (${\psi}$, ${\varphi}$)-WEAK CONTRACTIVE CONDITION TYPE

We establish a coincidence and a common fixed point result for four mappings involving a (, )-weak contractive condition type on a complete metric space. We take on and the same conditions given by Popescu [Fixed points for (, )-weak contractions, Appl. Math. Lett. 24 (2011), 1-4].

Some Fixed‐Point Results for a G‐Weak Contraction in G‐Metric Spaces

We introduce the concepts of a G‐weak contraction mapping of types A and B and we establish some fixed point theorems for a G‐weak contraction mapping of types A and B in complete G‐metric spaces. Our results generalize several well‐known comparable results in the literature.

Coupled Fixed Point Theorems under Weak Contractions

Cho et al. [Comput. Math. Appl. 61(2011), 1254–1260] studied common fixed point theorems on cone metric spaces by using the concept of c‐distance. In this paper, we prove some coupled fixed point theorems in ordered cone metric spaces by using the concept of c‐distance in cone metric spaces.

Coupled Coincidence Point Results for (ψ, α, β)‐Weak Contractions in Partially Ordered Metric Spaces

In this paper coupled coincidence points of mappings satisfying a nonlinear contractive condition in the framework of partially ordered metric spaces are obtained. Our results extend the results of Harjani et al. (2011). Moreover, an example of the main result is given. Finally, some coupled coincidence point results for mappings satisfying some contraction conditions of integral type in partially ordered complete metric spaces are deduced.

Common Fixed Points, Invariant Approximation and Generalized Weak Contractions

Sufficient conditions for the existence of a common fixed point of generalized -weakly contractive noncommuting mappings are derived. As applications, some results on the set of best approximation for this class of mappings are obtained. The proved results generalize and extend various known results in the literature.

Two-Dimensional Kinetic Analyses of Swallowing Using Videofluorographic Images of Dysphagia Patients

[Purpose] This studied examine the two-dimensional kinesis of swallowing by patients with dysphagia, based on the movements of contrast material using videofluorography, aiming to design curative programs for aspiration. Videofluorographic two-dimensional examinations of ten patients with aspiration, and another ten without aspiration were used for this study. [Methods] We converted the video record into static images and plotted hyoid bone and laryngeal kinesis on graphs, using two-dimensional image analysis software. Then, we conducted analyses of the trajectory patterns of the hyoid bone and the larynx, and pharyngeal transit time of the contrast material. [Results] Our two-dimensional method revealed significant differences between the two subject groups in maximal forward travel of the hyoid bone, maximal elevation of the larynx, and pharyngeal transit time. [Conclusion] Our findings suggest that aspiration may be caused by a weak pharyngeal contraction and weakened suprahyoid and infrahyoid muscles resulting in inferior kinesis of the epiglottis, and insufficient closure of the laryngeal introitus. For the treatment of aspiration, we believe the application of kinesiotherapy, electric stimulation therapy and replacement therapy should be clinically effective.

Relationship-Specificity, Contract Enforceability, and Income Smoothing

Contracting parties (e.g., the firm and its supplier) have cost-reducing incentives to make investments which support the unique transactions between them. However, to the extent that one party may renege on its contractual obligations, the other party incurring the cost of the relationship-specific investment bears additional risk and is less willing to invest (i.e., sub-optimal investment occurs). In countries where enforceability of explicit contracts is particularly weak, parties have incentives to signal their willingness to fulfill implicit claims and maintain long-term relationships. We predict that firms engage in income smoothing to send such a signal to their suppliers. Consistent with these expectations, we find that firms that both reside in countries with weak contract enforceability and operate in industries with a greater need for relationship-specific investments tend to smooth reported income more. We further decompose income smoothing into “informational” and “garbled” components and find that results are driven by the informational component of income smoothing. Our results support the important role that accruals play in providing information in the presence of incomplete contracts.

Coupled Fixed Point Theorems for Weak Contraction Mappings under F‐Invariant Set

We extend the recent results of the coupled fixed point theorems of Cho et al. (2012) by weakening the concept of the mixed monotone property. We also give some examples of a nonlinear contraction mapping, which is not applied to the existence of the coupled fixed point by the results of Cho et al. but can be applied to our results. The main results extend and unify the results of Cho et al. and many results of the coupled fixed point theorems.

Common fixed points for generalized contractive mappings in cone metric spaces

The purpose of this paper is to establish coincidence point and common fixed point results for four maps satisfying generalized weak contractions in cone metric spaces. Also, an example is given to illustrate our results.

Common Random Fixed Point Theorem for Generalized $(\psi,\varphi)$-Weak Contractions Random Operators

Common Random Fixed Point Theorem for Generalized $(\psi,\varphi)$-Weak Contractions Random Operators

Minimally modified LDL upregulates endothelin type B receptors in rat basilar artery

Minimally modified low density lipoprotein (mmLDL) is a well-known risk factor for cerebral vascular diseases and upregulation of endothelin type B (ETB) receptors plays key roles in the pathogenesis. The present study was designed to examine if mmLDL upregulated endothelin ETB receptors in basilar artery and its possible intracellular signaling molecular mechanisms. Rat basilar arteries were cultured for 24h in the presence of mmLDL with specific inhibitors. The artery contractile responses and receptor expressions of mRNA and protein were investigated using myograph system, real-time PCR and Western blot techniques, respectively. Results showed that ETB receptor agonist, sarafotoxin 6c induced a weak contraction in fresh basilar artery segments. After organ culture the contraction curve mediated by ETB receptor was shifted towards the left with an increased Emax of 88±6%. The mmLDL 10μg/mL further shifted the concentration–contractile curves towards the left with an increased Emax of 116±12%. The organ culture significantly increased ETB receptor mRNA and protein levels from fresh arteries, which was further enhanced by mmLDL. The staurosporine (PKC inhibitor), both SB386023 and U0126 (extracellular signal related kinases 1 and 2 inhibitor), and wedelolactone (NF-κB inhibitor) almost totally abolished organ culture-increased and mmLDL-increased contraction and expressions of endothelin ETB receptor. SP600125 (C-jun terminal kinase inhibitor) and SB203580 (p38 inhibitor) attenuated both organ cultured-induced and mmLDL-induced upregulation of endothelin ETB receptors. In conclusion, mmLDL upregulates ETB receptors of cerebral basilar artery via the PKC, MAPK and NF-κB signal pathways.

On the fixed point of (ψ−φ)-weak and generalized (ψ−φ)-weak contraction mappings

Let ( X , d ) be a complete metric space, and T : X ⟶ X be a ( ψ − φ ) -weak or generalized ( ψ − φ ) -weak contraction mapping, where ψ , φ : [ 0 , + ∞ ) ⟶ [ 0 , + ∞ ) are two mappings with ψ − 1 ( 0 ) = φ − 1 ( 0 ) = 0 , lim n → ∞ t n = 0 , if lim n → ∞ φ ( t n ) = 0 and ψ is continuous or ψ is monotone nondecreasing with φ ( a ) > ψ ( a ) − ψ ( a − ) for all a > 0 . Then T has a unique fixed point. Our results extend the previous results given by Rhoades (2001) [3], Dutta and Choudhury (2008) [4], Doric (2009) [5] and Popescu (2011) [6].

Fixed Point Theorems for Generalized $${\varphi}$$ -Weak Contractive Multivalued Maps on Metric and Ordered Metric Spaces

In this paper, we present some fixed point theorems for multivalued maps satisfying generalized \({\varphi }\) -weak contractions on metric and ordered metric spaces.

Human hand function: the limitations of brain and brawn

Human hand function: the limitations of brain and brawn

Y-WEAK CONTRACTIONS IN FUZZY METRIC SPACES

In this paper, the notion of $psi -$weak contraction cite{Rhoades} isextended to fuzzy metric spaces. The existence of common fixed points fortwo mappings is established where one mapping is $psi -$weak contractionwith respect to another mapping on a fuzzy metric space. Our resultgeneralizes a result of Gregori and Sapena cite{Gregori}.