Hypervalent iodine reagents constitute a powerful tool in modern synthetic organic chemistry, promoting several important reactions. One such reaction is the ring contraction of cycloalkenes and cycloalkanones promoted by iodine(III) compounds, such as iodobenzene diacetate, iodosylbenzene, iodotoluene difluoride, and [hydroxy(tosyloxy)- iodo]benzene (Koser' s reagent). This review covers all t...

Introduction Myocardial contraction is a cyclic event. Contraction delay can be described in terms of mechanical dispersion or phase delay of velocity, displacement and local deformation (strain) of segments in apical views of the left ventricle. Our hypothesis was that an increase in the standard deviation of phase would be seen as a consequence of myocardial scar and that this effect could be...

In this paper, we establish the existence of common coupled fixed point results for new Caristi type contraction of three covariant mappings in Bipolar metric spaces. Some interesting consequences of our results are achieved. Moreover, we give an illustration which presents the applicability of the achieved results.

[reaction: see text] A novel ring opening ring closing metathesis (ROM-RCM) was demonstrated for cyclic conjugated dienes, effecting the excision of a C(2)H(2) unit and a net ring contraction. Applying the ring contraction metathesis, new 14-membered ring macrolide antibiotics were synthesized in a single step from existing 16-membered ring macrolides. This new class of macrolide antibiotics wi...

We find a priori and a posteriori error estimates of the best proximity point for the Picard iteration associated to a cyclic contraction map, which is defined on a uniformly convex Banach space with modulus of convexity of power type.

In this paper, we introduce the results of best proximity point in G-metric spaces for the cyclic contraction mapping with an example that illustrates the usability of the obtained results. 2010 AMS Subject Classification: 41A65, 46B85, 47H25.

Based on a completely distributive lattice $M$, base axioms and subbase axioms are introduced in $M$-fuzzifying convex spaces. It is shown that a mapping $mathscr{B}$ (resp. $varphi$) with the base axioms (resp. subbase axioms) can induce a unique $M$-fuzzifying convex structure with  $mathscr{B}$ (resp. $varphi$) as its base (resp. subbase). As applications, it is proved that bases and subbase...

Inspired by the fact that the discontinuous mappings cannot be (Banach type) contractions and cyclic contractions need not be continuous, and taking into account that there are applications to integral and differential equations based on cyclic contractions, a new type of cyclic contraction mappings satisfying an implicit relation that involves a control function for a map in a metric space is ...