In this paper, we investigate relation between weak subdifferential and augmented normal cone. We define augmented normal cone via weak subdifferential and vice versa. The necessary conditions for the global maximum are also stated. We produce preliminary properties of augmented normal cones and discuss them via the distance function. Then we obtain the augmented normal cone for the indicator f...

‎The aim of this paper is to establish the equivalence between the concepts‎ ‎of an $S$-metric space and a cone $S$-metric space using some topological‎ ‎approaches‎. ‎We introduce a new notion of a $TVS$-cone $S$-metric space using‎ ‎some facts about topological vector spaces‎. ‎We see that the known results on‎ ‎cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained‎ from...

Our theorems are on ordered cone metric spaces which are not necessarily normal. In the end, we describe the application of the main results in the integral equation.Although Du in [W‎. ‎S‎. ‎Du‎, ‎A note on cone metric fixed point theory and its equivalence‎, ‎Nonlinear Analysis‎, ‎72(2010) 2259-2261.]‎, ‎showed that the fixed point results in the setting of cone...

nowadays, the use of innovative nano-technology in the food industry quality control has significantly increased and it is widely employed in numerous fields such as diagnosis of microbial toxin of foods using nano-biosensors, increasing food shelf-life with the help of nano-clay and nano-silver packaging, as well as changing some of the unpleasant organoleptic properties such as taste, color, ...

In this paper, we introduce the cone normed spaces and cone bounded linear mappings. Among other things, we prove the Baire category theorem and the Banach--Steinhaus theorem in cone normed spaces.

Nano-assisted inclusion separation of alkali metals from basic solutions was reported by an inclusion-facilitated emulsion liquid membrane process. The novelty of this study is application of nanobaskets of calixcrown in the selective and efficient separation of alkali metals as both the carrier and the surfactant. For this purpose, two diacids, p-tert-butylcalix[4]arene-1,2-crown-3 in the cone...

in this paper, we introduce the cone normed spaces and cone bounded linear mappings. among other things, we prove the baire category theorem and the banach--steinhaus theorem in cone normed spaces.