Weak Contraction Research Articles

Fixed Point Theorems for Mappings Satisfying Weak Nonexpansivity Condition (Weak Contractivity Condition) into (from) Cartesian Products Normed Spaces

This paper suggests new types of weak nonexpansive mappings defined from normed space X into its Cartesian product X × X, studies the main features of the fixed points for those mappings and extends the concept of (C)-contractivity condition introduced in some previous research papers. On other side, it introduces new types of contraction mappings with a mixed monotone property; the {a, b, c} M-first type and the {a, b, c} M-second type contractions, these types are defined from the Cartesian product space X × X into X, where X is a sequentially ordered Banach space, proves the existence of first-anti-second and second-anti-first couple fixed points of such types and generalizes some of the results given before.

Common Fixed Point Results for the (F, L)-Weak Contraction on Complete Weak Partial Metric Spaces

Common Fixed Point Results for the (F, L)-Weak Contraction on Complete Weak Partial Metric Spaces

Fixed Point Theory for Three φ–Weak Contraction Functions

In 2009 Qingnian Zhang and Yisheng Song proved fixed point theory for two φ–weak contraction functions. We generalize this result by finding fixed point and coincidence point for three single-valued φ–weak contraction T1, T2, T3 defined on a complete metric space.

The Effect of Acute Stress on Esophageal Motility and Gastroesophageal Reflux in Healthy Humans.

Background/AimsLittle research has been done to evaluate the effect of stress in exacerbating the symptoms associated with gastroesophageal reflux (GER). We aimed to investigate the effect of acute stress on esophageal motility and GER parameters in healthy volunteers.MethodsA total of 10 (M:F = 8:2, median age 34 years-old) healthy volunteers without any recurrent gastrointestinal symptoms participated in this study. They underwent esophageal high-resolution manometry with 10 wet swallows (Experiment I) and esophageal impedance-pH monitoring (Experiment II) in the basal period and in the stress period. In the stress period, either real stress or sham stress was given in a randomized cross-over design. The stress scores, symptom severity, and pulse rates were measured.ResultsThe stress scores and the severity of nausea were significantly greater under real stress, compared with sham stress. The percentages of weak, failed, rapid, premature, and hyper-contractile contractions were not significantly altered during real stress and during sham stress, compared with the basal period. The median resting pressure of the lower esophageal sphincter and distal contractile integral of esophageal contractions did not differ in the stress period, compared with the basal period. Contractile front velocity and distal latency of esophageal peristaltic contractions were significantly changed during real stress, which was not observed during sham stress. GER parameters were not significantly altered during real stress and during sham stress.ConclusionAlthough acute auditory and visual stress seems to affect esophageal body motility, it does not induce significant motor abnormalities or increase GER in healthy humans.

Common fixed point theorem for almost weak contraction maps with rational expression

Common fixed point theorem for almost weak contraction maps with rational expression

Some common fixed point theorems for tangential generalized weak contractions in metric-like spaces

In this paper we define the tangential property in partial metric spaces to prove a common fixed point theorems for two pairs of self mappings, which satisfying a generalized weak contractive condition as well as satisfying a generalized contraction, an example is given to illustrate ours results.

Some existence of coincidence point and approximate solution method for generalizedweak contraction in b-generalized pseudodistance fiunctionsy

The purpose of this article is to prove some coincidence point and approximate solution method for generalized weak contraction mapping in b??metric spaces by using the concept of b-generalized pseudodistance. Also, we give some examples to illustrate our main results.

Organising the unorganised: Role of platform intermediaries in the Indian real estate market

A large component of the Indian economy is still in the unorganised (or informal) sector. The emergence of new intermediaries leveraging the Internet has contributed significantly to organising the hitherto unorganised sector. We discuss the case of the Indian real estate industry and elucidate how Internet-based intermediaries have mitigated the problems associated with the unorganised nature of the industry. The three primary problems associated with the unorganised nature of the industry are adverse selection, moral hazard, and weak contract enforcement. Leaders representing four leading real estate platforms discuss how organising the real estate business as a platform business model helps mitigate these risks.

Tbx20 Is an Essential Regulator of Embryonic Heart Growth in Zebrafish.

The molecular mechanisms that regulate cardiomyocyte proliferation during embryonic heart growth are not completely deciphered yet. In a forward genetic N-ethyl-N-nitrosourea (ENU) mutagenesis screen, we identified the recessive embryonic-lethal zebrafish mutant line weiches herz (whz). Homozygous mutant whz embryos display impaired heart growth due to diminished embryonic cardiomyocyte proliferation resulting in cardiac hypoplasia and weak cardiac contraction. By positional cloning, we found in whz mutant zebrafish a missense mutation within the T-box 20 (Tbx20) transcription factor gene leading to destabilization of Tbx20 protein. Morpholino-mediated knock-down of Tbx20 in wild-type zebrafish embryos phenocopies whz, indicating that the whz phenotype is due to loss of Tbx20 function, thereby leading to significantly reduced cardiomyocyte numbers by impaired proliferation of heart muscle cells. Ectopic overexpression of wild-type Tbx20 in whz mutant embryos restored cardiomyocyte proliferation and heart growth. Interestingly, ectopic overexpression of Tbx20 in wild-type zebrafish embryos resulted, similar to the situation in the embryonic mouse heart, in significantly reduced proliferation rates of ventricular cardiomyocytes, suggesting that Tbx20 activity needs to be tightly fine-tuned to guarantee regular cardiomyocyte proliferation and embryonic heart growth in vivo.

The relevance of business practices in linking smallholders and large agro-businesses in Sub-Sahara Africa

Smallholders often have to certify according to international standards and produce under contract for large agro-businesses to access export markets. While mostly positive effects for the farmers have been found for contracts and certifications, often these effects do not persist because contracts fail and certifications are not renewed. We suggest that individual firm behavior is crucial for the long-term success of farmer-agro-business relationships. In this article, we use data of 386 smallholders in the pineapple export sector in Ghana, analyze them quantitatively and enrich it by a detailed case study of a large-scale agro-business in Ghana. The results show that, in an environment with weak contract enforcement, certification is an agent of change in farmer-agro-business relations and that building trust and aligning expectations of farmers and firms largely determine success. We conclude that individual firm behavior matters more than taken into account in previous research. Our case study shows that three ‘R’ – reliability, reputation and respect – constitute the basis for contract relationships that benefit all.

Common Fixed Point Results for \((\phi,\psi)\)-Weak Contraction Mappings via \(f\)-\(\alpha\)-Admissible Mappings in Intuitionistic Fuzzy Metric Spaces

In this paper, by using the concept of \(f\)-\(\alpha\)-admissible mappings, we prove common fixed point in intuitionistic fuzzy metric spaces. We also introduce the notion of \(f\)-\(\alpha\)-\(\phi\)-\(\psi\)-weak contraction mappings in intuitionistic fuzzy metric spaces. The presented theorems extend, generalize and improve the corresponding results which given in the literature.

A Case of Dystocia Induced by Misuse of Oxytocin in a Boerboel Bitch

A two year old boerboel bitch with dark greenish vaginal discharge and history of over 24 hours of difficult labor was presented to the Veterinary Teaching Hospital University of Ibadan for clinical examination and treatment. The owner had wrongfully given oxytocin after observation of signs of parturition. Following careful physical and clinical examinations of the bitch by Veterinary doctors, dystocia due to obstruction of maternal birth canal by a dead fetus was diagnosed. Treatment regimen was by digital manipulation which stimulated cervical dilatation and careful delivery of dead fetus via the vagina. Thereafter, oxytocin was administered to augment the bitch’s weak uterine contraction. Four weak puppies were delivered out of which three survived following adequate treatment.

Contract enforcement and R&D investment

Motivated by the differences in innovation across countries, this paper evaluates the role of contract enforcement for R&D investments. We find empirical evidence that weak contract enforcement is associated with lower R&D investment: R&D intensity in an industry increases with the quality of the judicial system. This effect is particularly strong in industries that cannot buy inputs on competitive markets and thus depend more on contracts to acquire inputs. In line with this, we show that contract enforcement is particularly important in industries in which vertical integration is not a viable option.

A common fixed point theorem for mappings satisfying (y,j)-weak contractions satisfying rational expressions in ordered partial metric spaces

A common fixed point theorem for mappings satisfying (y,j)-weak contractions satisfying rational expressions in ordered partial metric spaces

Pulse Duration as Well as Current Direction Determines the Specificity of Transcranial Magnetic Stimulation of Motor Cortex during Contraction.

Previous research suggested that anterior-posterior (AP) directed currents induced by TMS in motor cortex (M1) activate interneuron circuits different from those activated by posterior-anterior currents (PA). The present experiments provide evidence that pulse duration also determines the activation of specific interneuron circuits. To use single motor unit (SMU) recordings to confirm the difference in onset latencies of motor-evoked potentials (MEPs) evoked by different current directions and pulse durations: AP30, AP120, PA30 and PA120. To test whether the amplitude of the MEPs is differentially influenced by somatosensory inputs from the hand (short-latency afferent inhibition, SAI), and examine the sensitivity of SAI to changes in cerebellar excitability produced by direct current stimulation (tDCSCb). Surface electromyograms and SMUs were recorded from the first dorsal interosseous muscle. SAI was tested with an electrical stimulus to median or digital nerves ~20-25 ms prior to TMS delivered over the M1 hand area via a controllable pulse parameter TMS (cTMS) device. SAI was also tested during the application of anodal or sham tDCSCb. Because TMS pulse specificity is greatest at low stimulus intensities, most experiments were conducted with weak voluntary contraction to reduce stimulus threshold. AP30 currents recruited the longest latency SMU and surface MEP responses. During contraction SAI was greater for AP30 responses versus all other pulses. Online anodal tDCSCb reduced SAI for the AP30 currents only. AP30 currents activate an interneuron circuit with functional properties different from those activated by other pulse types. Pulse duration and current direction determine what is activated in M1 with TMS.

Does weak contract enforcement affect firm size? Evidence from the neighbour’s court

Poor contract enforcement can importantly affect firms’ incentives to grow. We investigate the causal effect of the weakness of contract enforcement on average firm size across Italian municipalities, exploiting spatial discontinuities in court jurisdictions for identification. Italy provides an ideal environment for this exercise, as it displays wide variation in judicial efficiency across courts, while the allocation of municipalities to jurisdictions is a historical legacy and does not overlap with other political or economic discontinuities. Our estimates indicate that reducing the length of judicial proceedings (i.e. improving contract enforceability) by 10% at court level leads to a 2% increase in average size of local firms. The outcome on turnover growth is of the same magnitude, suggesting that the effect operates at the intensive margin.

Common Fixed Point Theorems for Generalized Quadratic $ (\psi_{1},\psi_{2},\phi)$-Weak Contraction in Complete Metric Spaces

Common Fixed Point Theorems for Generalized Quadratic $ (\psi_{1},\psi_{2},\phi)$-Weak Contraction in Complete Metric Spaces

Fixed point Theorem Satisfying Weak Integral Type Contraction in Generalized Metric Spaces

Fixed point Theorem Satisfying Weak Integral Type Contraction in Generalized Metric Spaces

Best proximity results: optimization by approximate solutions

AbstractIn this paper we utilize a generalized weakly contractive mapping to establish some best proximity point results which are global optimization results for finding the minimum distances between two sets. Amongst many approaches to this problem, we adopt the approach where the problem is treated as that of finding global optimal approximate solution of the fixed point equation for the generalized weak contraction mapping. We use three control functions to define such mappings. The results are obtained in metric spaces with a partial ordering defined therein. There is a blending of analytic and order theoretic approaches in the proofs. The uniqueness is obtained by imposing some order theoretic conditions additionally. There are several corollaries. An illustration of the main theorem through an example is given which also shows that the corollaries are properly contained in the main theorem.

Positive definite solution of a nonlinear matrix equation

Using fixed point theory, we present a sufficient condition for the existence of a positive definite solution of the nonlinear matrix equation \({X = Q \pm \sum^{m}_{i=1}{A_{i}}^*F(X)A_{i}}\), where Q is a positive definite matrix, Ai’s are arbitrary n × n matrices and F is a monotone map from the set of positive definite matrices to itself. We show that the presented condition is weaker than that presented by Ran and Reurings [Proc. Amer. Math. Soc. 132 (2004), 1435–1443]. In order to do so, we establish some fixed point theorems for mappings satisfying (\({\psi, \phi}\))-weak contractivity conditions in partially ordered G-metric spaces, which generalize some existing results related to (\({\psi, \phi}\))-weak contractions in partially ordered metric spaces as well as in G-metric spaces for a given function f. We conclude, by presenting an example, that our fixed point theorem cannot be obtained from any existing fixed point theorem using the process of Jleli and Samet [Fixed Point Theory Appl. 2012 (2012), Article ID 210].