Weak Contraction Research Articles

Strong convergence theorem of a new iterative method for weak contractions and comparison of the rate of convergence in Banach space

In this paper, we first construct a new iteration method for approximating fixed points of a class of weak contractions in a Banach space and then prove strong convergence theorem of the proposed method under some control conditions. It is shown that our iteration method converges faster than Noor iteration. Moreover, we give some numerical example for comparing the rate of convergence between the Noor iteration and our iteration.

Intimate Mappings Satisfying Generalized and#216;-Weak Contraction Involving Cubic Terms of Metric Function

Intimate Mappings Satisfying Generalized and#216;-Weak Contraction Involving Cubic Terms of Metric Function

Best proximity point theorems for G-proximal weak contractions in complete metric spaces endowed with graphs

In this paper, the existence of best proximity point theorems for two new types of nonlinear non-self mappings in a complete metric space endowed with a directed graph are established. Our main results extend and generalize many known results in the literatures. As a special case of the main results, the best proximity point theorems on partially ordered sets are obtained.

Some coincidence point theorems in ordered metric spaces via w-distances

The purpose of this paper is to prove some existence theorems of coincidence points for generalized weak contractions in the setting of partially ordered sets with a metric via w-distances and give some example to illustrate our main results.

Best proximity point for proximal Berinde nonexpansive mappings on starshaped sets

In this paper, we introduce the new concept of proximal mapping, namely proximal weak contractions and proximal Berinde nonexpansive mappings. We prove the existence of best proximity points for proximal weak contractions in metric spaces, and for proximal Berinde nonexpansive mappings on starshape sets in Banach spaces. Examples supporting our main results are also given. Our main results extend and generalize some of well-known best proximity point theorems of proximal nonexpansive mappings in the literatures.

Multi-Segmental Intramedullary Epidermoid Cyst Causing Low Back Pain and Urologic Dysfunction

Introduction: Epidermoid cysts (ECs) are rare, slow growing tumors which usually affect lumbosacral area as an extramedullary lesion and mostly associated with spinal malformations. In this report we describe a very rare case of multi-segmental intramedullary EC. Case Presentation: A 42- year-old male presented with low back pain and paresthesia of left lower limb and also intermittent urinary retention. Urodynamic study showed weak contractions in bladder. MRI demonstrated multi-segmental lobulated intramedullary lesion extending from C7 to L2, which has high intensity on both T1 and T2-weighted images. Laminectomy of T11-L3 for symptomatic parts of the lesion and subtotal resection of the tumor was performed and histopathological investigation confirmed EC. Conclusions: Prompt evaluation of every patient with combination of neurological and urologic disturbances should be carried out. This report suggests that rare intraspinal tumors such as EC may affect multiple locations of the spinal cord, thus appropriate surgical intervention may prevent unwanted sequelae.

Notes on multidimensional fixed-point theorems

Abstract In this paper we prove the existence and uniqueness of coincident (fixed) points for nonlinear mappings of any number of arguments under a (ψ, θ, φ)-weak contraction condition without O-compatibility. The obtained results extend, improve and generalize some well-known results in the literature to be discussed below. Moreover, we present an example to show the efficiency of our results.

$$\varphi $$ φ -Best proximity point theorems and applications to variational inequality problems

The main concern of this study is to introduce the notion of $$\varphi $$ -best proximity points and establish the existence and uniqueness of $$\varphi $$ -best proximity point for non-self mappings satisfying $$(F,\varphi )$$ -proximal and $$(F,\varphi )$$ -weak proximal contraction conditions in the context of complete metric spaces. Some examples are supplied to support the usability of our results. As applications of the obtained results, some new best proximity point results in partial metric spaces are presented. Furthermore, sufficient conditions to ensure the existence of a unique solution for a variational inequality problem are also discussed.

The existence and uniqueness of the solution for nonlinear Fredholm and Volterra integral equations together with nonlinear fractional differential equations via w-distances

In this work, we establish new fixed point theorems for w-generalized weak contraction mappings with respect to w-distances in complete metric spaces by using the concept of an altering distance function. As an application, we use the obtained results to aggregate the existence and uniqueness of the solution for nonlinear Fredholm integral equations and Volterra integral equations together with nonlinear fractional differential equations of Caputo type.

Non-self-similar sets in [0,1]N of arbitrary dimension

We consider [0,1]N, the unit cube of RN, N⩾1. Let S={S1,…,SM} be a finite set of contraction maps from X to itself. A non-empty subset E of X is an attractor (or an invariant set) for the iterated function system (IFS) S if E=∪i=1MSi(E). We construct, for each s∈]0,N], a nowhere dense perfect set E contained in [0,1]N, with Hausdorff dimension s, which is not an attractor for any iterated function system composed of weak contractions from [0,1]N to itself.

Coincidence point results via generalized (ψ,ϕ)-weak contractions in partial ordered b-metric spaces with application

Coincidence point results via generalized (ψ,ϕ)-weak contractions in partial ordered b-metric spaces with application

Credit Constraint Exports in Countries with Different Degrees of Contract Enforcement

We theoretically consider firms’ export decisions in a heterogeneous firm framework. The paper assumes firms have idiosyncratic productivity levels and are credit-constrained in the export market. Firms in different countries have different degrees of credit constraints. Because of imperfect financial markets, firms might not be able to get the financial support to export even although they are profitable enough from the foreign market. In a country with strong contract enforcement, firms are more likely to export and export to more destinations; while in a country with weak contract enforcement, firms are more likely to be constrained by liquidity and export to fewer destinations. However, for those firms whose productivity is very low or very high, these influences do not exist. Moreover, we consider technology shocks and illustrate that technology shocks will further impede firms’ export decisions.

Common fixed point theorems without continuity and compatible property of maps

In this paper, without assuming continuity, commutativity and compatibility of self maps, some common fixed theorem for weak contraction of integral type in complete metric spaces are proved. An example and some remarks are also given to justify that our contraction is new and weaker than other existing contractions.

Age-dependent functional crosstalk between cardiac fibroblasts and cardiomyocytes in a 3D engineered cardiac tissue.

Previous studies have shown that cardiomyocytes and fibroblasts in the heart interact through direct contacts, paracrine factors, and matrix-mediated crosstalk. However, whether cardiac fibroblasts of different ages distinctly impact cardiomyocyte function remains elusive. We employed a tissue-engineered hydrogel-based co-culture system to study interactions of cardiomyocytes with fetal or adult cardiac fibroblasts. We show that the age of cardiac fibroblasts is a strong determinant of the structure, function, and molecular properties of engineered cardiac tissues and that key features of fibrotic myocardium are replicated by supplementing cardiomyocytes with expanded adult but not fetal fibroblasts. These findings relate to implantation of stem cell-derived cardiomyocytes in adult myocardium and warrant further studies of how age and source of non-myocytes impact cardiac function and maturation.

Large Positive Thermal Expansion and Small Band Gap in Double-ReO3-Type Compound NaSbF6.

Double-ReO3-type structure compound NaSbF6 undergoes a low-temperature rhombohedral to high-temperature cubic phase between 303 and 323 K, as revealed by temperature-dependent X-ray diffractions. Although many double-ReO3-type fluorides exhibit either low thermal expansion or negative thermal expansion (NTE), NaSbF6 exhibits positive thermal expansion (PTE) with a large volumetric coefficient of thermal expansion, αv = 62 ppm/K, in its cubic phase. Raman spectroscopy reveals that the low-frequency transverse vibration of fluorine atoms is stiffened in NaSbF6, compared with the typical NTE compound CaZrF6 with the same structure. The related weak contraction associated with the polyhedral rocking would be overcome by the notable elongation of the Na-F bond length on heating, thus leading to the large volumetric PTE. Unlike ScF3 and CaZrF6 which are insulators with a wide band gap, a relative small band gap of 3.76 eV was observed in NaSbF6. The small band gap can be attributed to the hybridization between the Sb 5s and F 2p orbitals.

WEAK SELF-SIMILAR SETS IN SEPARABLE COMPLETE METRIC SPACES

Self-similarity is a common tendency in nature and physics. It is wide spread in geo-physical phenomena like diffusion and iteration. Physically, an object is self-similar if it is invariant under a set of scaling transformation. This paper gives a brief outline of the analytical and set theoretical properties of different types of weak self-similar sets. It is proved that weak sub self-similar sets are closed under finite union. Weak sub self-similar property of the topological boundary of a weak self-similar set is also discussed. The denseness of non-weak super self-similar sets in the set of all non-empty compact subsets of a separable complete metric space is established. It is proved that the power of weak self-similar sets are weak super self-similar in the product metric and weak self-similarity is preserved under isometry. A characterization of weak super self-similar sets using weak sub contractions is also presented. Exact weak sub and super self-similar sets are introduced in this paper and some necessary and sufficient conditions in terms of weak condensation IFS are presented. A condition for a set to be both exact weak super and sub self-similar is obtained and the denseness of exact weak super self similar sets in the set of all weak self-similar sets is discussed.

On Fixed Point Theorem of C Class Functions - B Weak Cyclic Mappings

New B-𝔘-cyclic weak contraction C-class function concept has been introduced, B-𝔘-cyclic weak F-φ-Φ-contraction types of mapping are defined and the existence of fixed point for such types has been proved. These results mainly generalize fixed point theorems in some previous research papers.

Fixed point results for generalized [formula omitted]-weak contractions with an application to system of non-linear integral equations

The aim of this paper is to prove fixed point results under (ψ,ϕ)-weak contractive condition for continuous weak compatible mappings in ordered b-metric spaces. The results proved herein generalize, modify and unify some recent results of the existing literature. An application demonstrating the usability of our established results is also discussed besides furnishing an illustrative example.

Round Table - 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.

P159 Specific and non-specific inhibition of interneurons circuits during motor preparation and suppression

Introduction Corticospinal excitability is transiently suppressed during motor preparation (Greenhouse et al., 2015 ) and when cancelling a prepared movement (Hoshiyama et al., 1997 ). Because MEPs are suppressed even in task-irrelevant muscles Greenhouse et al., 2015 , Hoshiyama et al., 1997 ), it has been proposed that there is a “global” inhibitory signal (Greenhouse et al., 2015) . Objectives We tested the whether the inhibition is global or specific to different excitatory interneuron circuits in primary motor cortex (M1). Materials & methods A controllable pulse parameter TMS (cTMS; Rogue Resolutions Ltd.) device was used to activate distinct interneuron circuits in M1 by changing the coil orientation (posterior–anterior, PA; anterior–posterior, AP) and TMS pulse width (30–120 μs). Motor evoked potentials (MEPs) were elicited in the first dorsal interosseous muscle(s) using short AP- (AP30) and long PA-directed (PA120) pulses at various stages during: (1) a left/right choice reaction time task (CRTT) in which a non-informative warning cue appeared 0.5 s prior to the imperative signal indicated the required response; and (2) a Go/No-Go task in which a non-informative warning cue appeared 2 s prior to a Go or No-Go signal indicating to respond or not respond. Because TMS pulse specificity is greatest at low stimulus intensities, experiments were conducted with weak voluntary contraction (5–10% maximum) to reduce stimulus threshold. Results AP30 pulses evoked MEPs with a longer latency than PA120 pulses, confirming that different excitatory interneurons were recruited by the different pulse. [RH1] In the CRTT, the amplitude of AP30-evoked MEPs was suppressed at the time of the imperative stimulus in both responding and non-responding hands, whereas responses to PA120 stimuli were unaffected (Fig. 1A) Download : Download high-res image (366KB) Download : Download full-size image .[RH2] In the Go/No-Go task, AP30 and PA120 MEPs were suppressed to a similar extent in the No-Go condition near to the expected onset of movement (Fig. 1B). Conclusion During motor preparation for the CRTT there was a selective suppression of one interneuron circuit in M1. In contrast, a global inhibition of corticospinal excitability was observed following a decision not to move. The implication is that the mechanisms underlying each form of inhibition are at least partially distinct.