Abstract In this paper, we introduce the notions of proximal Berinde g -cyclic contractions two non-self-mappings and -contractions, called contraction first second kind. Coincidence best proximity point theorems for these types mappings in a metric space are presented. Some examples illustrating our main results also given. Our extend generalize many existing literature.

244 gallbladder. Like smooth mnscle, canalicular bile tlow is energy dependent. Agents tltat alter the antot, nt of ATI' in the cell sap have a similar effect on bile tlow rate. The rate of bile flow is modulated b)' a hormotte-receptor interaction attalogous to tire contraction-relaxation c)'cle of smooth muscle in which cAMI' and Ca + + are tire chief determinants. The same determinants are t...

In this article, we introduce the concept of weak F?m,?-contractions on relation-theoretic m-metric spaces and establish related fixed point theorems, where ? is a control function ? relation. Then, detail some results for cyclic-type F?m,?-contraction mappings. Finally, demonstrate illustrative examples discuss upper lower solutions Volterra-type integral equations form ??=?0?A?,?,??m?+??,??0,1.

Cholecystokinin-octapeptide (CCK-OP) evoked contraction and 3H-acetylcholine (3H-ACh) release of the muscle strip of the guinea pig gallbladder were studied. Although hexamethonium (10(-5) M) or tetrodotoxin (10(-6) M) had no effect on CCK-OP (10(-8) M) evoked contraction and 3H-ACh release, Ca-free medium almost completely abolished CCK-OP (10(-8) M) evoked 3H-ACh release. In Ca-free medium co...

We show that if the cochain complex computing Ext groups (in category of modules over Hopf algebroids) admits a cocyclic structure, then noncommutative Cartan calculus structure on Tor dualises in cyclic sense to Coext Cotor. More precisely, duals chain resp. spaces two classical derived functors lead complexes compute more exotic ones, giving opposite module an operad with multiplication induc...