Best proximity point theorems for $ \alpha^{+} F, (\theta-\phi )$-proximal contraction

In this paper, inspired by the idea of Suzuki type $ \alpha^{+} F$-proximal contraction in metric spaces, we prove a new existence of best proximity point for Suzuki type $ \alpha^{+} F$-proximal contraction and $ \alpha^{+} (\theta-\phi )$-proximal contraction defined on a closed subset of a complete metric space. Our theorems extend, generalize, and improve many existing results.

Best Proximity Point Theorems for Single and Multivalued Mappings in Fuzzy Multiplicative Metric Space

In this paper, we introduce fuzzy multiplicative metric space and prove some best proximity point theorems for single-valued and multivalued proximal contractions on the newly introduced space. As corollaries of our results, we prove some fixed-point theorems. Also, we present best proximity point theorems for Feng-Liu-type multivalued proximal contraction in fuzzy metric space. Moreover, we illustrate our results with some interesting examples.

Existence of best proximity points satisfying two constraint inequalities

In this paper, we prove the existence of best proximity point and coupled best proximity point on metric spaces with partial order for weak proximal contraction mappings such that these critical points satisfy some constraint inequalities.

A discussion on the coincidence quasi-best proximity points

In this paper, we first introduce a new class of the pointwise cyclic-noncyclic proximal contraction pairs. Then we consider the coincidence quasi-best proximity point problem for this class. Finally, we study the coincidence quasi-best proximity points of weak cyclic-noncyclic Kannan contraction pairs. We consider an example to indicate the validity of the main result.

Best proximity point of modified Suzuki-Edelstein-Geraghty type proximal contractions

In this paper, we introduce the notion of modified Suzuki-Edelstein-Geraghty proximal contraction and prove the existence and uniqueness of best proximity point for such mappings. Our results extend and unify many existing results in the literature. We draw corollaries and give illustrative example to demonstrate the validity of our result.

Multi-step inertial proximal contraction algorithms for monotone variational inclusion problems

"In this article, we introduce the multi-step inertial proximal contraction algorithms (MiPCA) to approximate a zero of the sum of two monotone operators, with one of the two operators being monotone and Lipschitz continuous. The weak convergence of the MiPCA is shown under the summability condition formulated in terms of the iterative sequence in a Hilbert space setting. We also investigate the unconditional convergence of the one-step inertial proximal contraction algorithm. Finally, numerical experiments are given to illustrate the advantage of the multi-step inertial proximal contraction algorithms."

A Discussion on the Existence of Best Proximity Points That Belong to the Zero Set

In this paper, we investigate the existence of best proximity points that belong to the zero set for the α p -admissible weak ( F , φ ) -proximal contraction in the setting of M-metric spaces. For this purpose, we establish φ -best proximity point results for such mappings in the setting of a complete M-metric space. Some examples are also presented to support the concepts and results proved herein. Our results extend, improve and generalize several comparable results on the topic in the related literature.

ALTERED ESOPHAGEAL MOTILITY DURING PERCEPTION OF BOLUS TRANSIT IN HEALTHY VOLUNTEERS

ABSTRACT BACKGROUND: The perception of bolus transit through the thoracic esophagus may be caused by altered esophageal anatomy and function. OBJECTIVE: To evaluate the hypothesis that, in healthy volunteers, swallows followed by perception of esophageal bolus transit are associated with changes in esophageal motility. METHODS: Simultaneous evaluation of motility and perception of esophageal bolus transit was performed in 22 healthy volunteers. Esophageal motility was evaluated by high-resolution manometry with a 32-channel solid state catheter. Each volunteer performed, in the sitting position, 10 swallows of a 5 mL bolus of saline and 10 swallows of pieces of 1 cm3 of bread, with an interval of at least 30 seconds between swallows. After each swallow the volunteers were asked about the perception of bolus transit through the esophagus. RESULTS: Perception of bolus transit occurred in 11.7% of liquid swallows and in 48.1% of solid swallows. In liquid swallows the perception was associated with higher distal contractile integral and shorter proximal contraction length. Perception of solid bolus transit was associated with a longer distal latency, longer proximal contraction length, lower proximal contractile integral and shorter proximal contraction duration. CONCLUSION: The perception of swallowed bolus transit through the esophagus in healthy individuals is more frequent with solid than liquid swallows and is associated with changes in proximal esophageal contractions.