Some fixed point theorems for weakly compatible mappings in Non-Archimedean Menger probabilistic metric spaces via common limit range property

In this paper, we utilize the notion of common limit range property in Non-Archimedean Menger PM-spaces and prove some fixed point theorems for two pairs of weakly compatible mappings. Some illustrative examples are furnished to support our results. As an application to our main result, we present a common fixed point theorem for four finite families of self mappings. Our results improve and extend several known results existing in the literature

Gregus type fixed point theorems for weakly subsequentially continuous mappings satisfying strict contractive condition of integral type

In the present  paper, we prove two common fixed point theorems of Gregus type for two pairs of self mappings satisfying strict contractive condition of integral type by using the weak subsequential continuity property with compatibility of type $(E)$ due to Singh and Mishra [Coincidence and fixed points of reciprocally continuous and compatible hybrid maps, Internat. J. Math. Math. Sci. 10 (2002), 627-635] in metric spaces. Our results improve and the results of Chauhan et al. [Some integral type fixed-point theorems and an application to systems of functional equations, Vietnam J. Math. 42 (2014), no. 1, 17-37] and relevant literature

How familiarity warps representation in the face space

Recognition of familiar as compared to unfamiliar faces is robust and resistant to marked image distortion or degradation. Here we tested the flexibility of familiar face recognition with a morphing paradigm where the appearance of a personally familiar face was mixed with the appearance of a stranger (Experiment 1) and the appearance of one's own face with the appearance of a familiar face and the appearance of a stranger (Experiment 2). The aim of the two experiments was to assess how categorical boundaries for recognition of identity are affected by familiarity. We found a narrower categorical boundary for the identity of personally familiar faces when they were mixed with unfamiliar identities as compared to the control condition, in which the appearance of two unfamiliar faces was mixed. Our results suggest that familiarity warps the representational geometry of face space, amplifying perceptual distances for small changes in the appearance of familiar faces that are inconsistent with the structural features that define their identities. Significance statement Familiar faces are recognized robustly despite image degradation, differences in lighting, head position, or distance. Here, we investigated the flexibility of familiar face recognition with two separate experiments using a morphing paradigm. Our data suggest that a familiar face occupies a sector of perceptual face space that is expanded relative to its extent based on differences in measured physical similarity. This expansion in representational space may be part of a more general mechanism that could explain how learning can facilitate processing of behaviorally relevant stimuli

Fixed Points of Weakly Compatible Mappings Using Common (E.A) Like property

The aim of this paper is to prove common fixed point theorems in Menger spaces using implicit relation and common (E.A) like property. An example is derived to support our main result. We extend our result to four finite families of self mappings. As an application of our main result, we prove an integral type common fixed point theorem satisfying ψ-contraction condition in Menger space. Our results improve some recent results in Menger spaces

Study of clinical profile of patients of bipolar mood disorder with and without substance abuse and clinical course variables in the substance abusing bipolar group in one of the tertiary care centre of North India

Background: Bipolar disorder is the sixth leading cause of disability worldwide and has a lifetime prevalence of about 3% in general population. In patients with bipolar disorder there was 58 % lifetime prevalence of co-occurring alcohol abuse and a 38 % lifetime prevalence of co-occurring other substance abuse. Substance abuse interferes with treatment and management approaches of the bipolar disorder.Methods: A cross sectional observational study of 120 male patients divided in substance abusing (60) and non-substance abusing groups (60) with bipolar disorder according to DSM-V, who met the Inclusion criteria . A written informed consent was obtained from the patients and/ or their family members. Patient’s information was recorded on the socio-demographic and clinical profile sheet .Thereafter, YMRS or HAM-D scales were applied as per the phase of the illness.Results: Most of the patients were between 15-25 years in SAB group and 35-50 years in NSAB group, educated, semiskilled and married. Tobacco abuse was the commonest followed by cannabis and alcohol abuse. The mean duration of hospital stay in SAB group was 41.40 days and in NSAB group was 43.20 days. Dysphoric mania, aggressive behavior and suicidal attempts were more in SAB group. Mean total YMRS score of SAB group was greater than NSAB group.Conclusions: Maximum patients had onset of substance abuse before the onset of affective symptoms. Manic symptomatology was more severe in substance abusing group

A Hybrid Common Fixed Point Theorem under Certain Recent Properties

We prove a common fixed point theorem for a hybrid pair of occasionally coincidentally idempotent mappings via common limit range property. Our result improves some results from the existing literature, especially the ones contained in Sintunavarat and Kumam (2009). Some illustrative and interesting examples to highlight the realized improvements are also furnished

Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces

The aim of this paper is to prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space by using the (CLRg) property. An example is also furnished which demonstrates the validity of our main result. As an application to our main result, we present a fixed point theorem for two finite families of self mappings in fuzzy metric space by using the notion of pairwise commuting. Our results improve the results of Sedghi, Shobe and Aliouche [A common fixed point theorem for weakly compatible mappings in fuzzy metric spaces, Gen. Math. 18(3) (2010), 3-12 MR2735558]

Unified Fixed Point Theorems via Common Limit Range Property in Modified Intuitionistic Fuzzy Metric Spaces

The purpose of this paper is to emphasize the role of “common limit range property” to ascertain the existence of common fixed points in modified intuitionistic fuzzy metric spaces enjoying an implicit function utilized in Tanveer et al. (2012) and Imdad et al. (2012). As an application to our main result, we derive a fixed point theorem for finite families of self-mappings. We also give some examples which demonstrate the validity of the hypotheses and degree of generality of our main results. Our results improve and extend several previously known fixed point theorems of the existing literature