Simulations functions and Geraghty type results

We concern this manuscript with Geraghty type contraction mappings via simulation functions and pull down some sufficient conditions for the existence and uniqueness of point of coincidence for several classes of mappings involving Geraghty functions in the setting of metric spaces. These findings touch up many of the existing results in the literature. Additionally, we elicit one of our main result by a non-trivial example and pose an interesting open problem for the enthusiastic readers.

TITIK TETAP PERSEKUTUAN EMPAT PEMETAAN KONTRAKTIF PADA RUANG METRIK CONE

Huang Long Guang dan Zhang Xian pada tahun 2006 telah memperkenalkan metrik yang lebih baru yang disebut metrik cone. Suatu himpunan tak kosong X yang dilengkapi metrik cone d disebut ruang metrik cone. Suatu pemetaan memiliki titik tetap yang tunggal jika pemetaan tersebut merupakan pemetaan kontraktif. Konsep titik tetap persekutuan di ruang metrik cone juga harus memenuhi beberapa kondisi pemetaan yang bersifat coincidence point, point of coincidence, dan kompatibel lemah. Penelitian ini mengkaji titik tetap persekutuan untuk empat pemetaan yang kontraktif pada ruang metrik cone. Hasil penelitian ini menunjukkan bahwa empat pemetaan S, T, I dan J memiliki titik tetap persekutuan yang tunggal pada ruang metrik cone.Kata Kunci: ruang metrik cone, titik tetap persekutuan, pemetan kontraktif, coincidence point, point of coincidence, kompatibel lemah

The Effect of Transient Location on the Resolution of Bistable Visual and Audiovisual Motion Sequences

We examined the attention and inference accounts of audiovisual perception using the stream/bounce display, a visual stimulus wherein two identical objects move toward each other, completely superimpose, then move apart. This display has two candidate percepts: stream past each other or bounce off each other. Presented without additional visual or auditory transients, the motion sequence tends to yield the streaming percept, but when coupled with a tone or flash at the point of coincidence, the response bias flips toward bouncing. We explored two competing accounts of this effect: the attentional hypothesis and the inference hypothesis. Participants watched a series of motion sequences where a transient, when present, occurred at the moment of coincidence either colocalised with the motion sequence (congruent presentation) or on the opposite side of the display (incongruent presentation). Assuming the spotlight or zoom lens metaphor, an attentional account predicts that incongruent presentations should be associated with a higher percentage of bouncing responses than congruent presentations, while the inferential account predicts the opposite effect. No effect was found for tone-only trials. However, in trials containing a visual transient, results showed higher proportions of bounce responses within congruent over incongruent presentations, favouring the inference hypothesis over a spotlight or zoom lens attentional account.

Streaming, Bouncing, and Rotation: The Polka Dance Stimulus

When the objects in a typical stream-bounce stimulus are made to rotate on a circular trajectory, not two but four percepts can be observed: streaming, bouncing, clockwise rotation, and counterclockwise rotation, often with spontaneous reversals between them. When streaming or bouncing is perceived, the objects seem to move on individual, opposite trajectories. When rotation is perceived, however, the objects seem to move in unison on the same circular trajectory, as if constituting the edges of a virtual pane that pivots around its axis. We called this stimulus the Polka Dance stimulus. Experiments showed that with some viewing experience, the viewer can “hold” the rotation percepts. Yet even when doing so, a short sound at the objects’ point of coincidence can induce a bouncing percept. Besides this fast percept switching from rotation to bouncing, an external stimulus might also induce slower rotation direction switches, from clockwise to counterclockwise, or vice versa.

Simulation type functions and coincidence points

In this paper, we obtain some sufficient conditions for the existence and uniqueness of point of coincidence by using simulation functions in the context of metric spaces and prove some interesting results. Our results generalize the corresponding results of [5, 8, 13, 14, 16] in several directions. Also, we provide an example which shows that our main result is a proper generalization of the result of Jungck [American Math. Monthly 83(1976) 261-263], L-de-Hierro et al. [J. Comput. Appl. Math 275(2015) 345-355] and of Olgun et al. [Turk. J. Math. (2016) 40:832-837].

The Point of Coincidence and Common Fixed Point for Three Mappings in Cone Metric Spaces

The aim of this paper is to present the point of coincidence and common fixed point for three mappings in cone metric spaces over normal cone which satisfy a different contractive condition. Our result generalizes the recent related results proved by Stojan Radenović (2009) and Rangamma and Prudhvi (2012).