Agarase is a promising biocatalyst for several industrial applications. Agarase production was evaluated by the marine fungus Dendryphiella arenaria utilizing Palisada perforata as a basal substrate in semi-solid state fermentation. Seaweed biomass, glucose, and sucrose were the most significant parameters affecting agarase production, and their levels were further optimized using Box-Behnken design. The maximum agarase activity was 7.69 U/mL. Agarase showed a degree of thermostability with half-life of 99 min at 40 °C, and declining to 44.72 min at 80 °C. Thermodynamics suggested an important process of protein aggregation during thermal inactivation. Additionally, the enzymatic saccharification of the seaweed biomass using crude agarase was optimized with respect to biomass particle size, solid/liquid ratio, and enzyme loadings. The amount of biosugars obtained after optimization was 26.15 ± 1.43 mg/g. To the best of our knowledge, this is the first report on optimization of agarase in D. arenaria.

The aim of this work is to obtain some existence and uniqueness fixed point theorems for mixed gmonotone mapping in any number of variables under general contractive conditions in partially ordered metric spaces by using the condition of weak compatibility. Our results are different, more natural and generalizations of many results on multidimensional fixed points. For illustration of the effectiveness of our generalizations, some examples are equipped in this paper

The aim of this paper is to prove some common and coupled random xed point theorems for a pair of weakly monotone random operators satisfying some rational type contraction in the setting of partially ordered S-metric space. Our results extend and generalize many existing results in the literature. Moreover, an example is given to support our results. Finally, the results are used to prove the existence and uniqueness of solution of some random functional equations.

In present paper we introduce the concepts of mixed g-monotone property and Delta g-symmetric property, where g is single valued mapping, for multi-valued mapping under any number of variables and use it to obtain some existence and uniqueness fixed points for hybrid pair of mappings under general contractive conditions in partially ordered metric spaces. Our results are generalizations of several results in this direction. We equipped this paper with examples in order to illustrate the effectiveness of our generalizations.

In this paper, we introduce the notion of mixed weakly monotone property for two hybrid pairs (S, g) and (T, g) each of them consists of multi-valued mapping S or T: X^{n}-> CB(X) and single valued mapping g: X-> X defined on partially ordered metric space and then we prove coincidence and common fixed point theorems for two hybrid pairs under different contractive conditions. These theorems extend and generalize very recent results that can be found in [12] and many others.

In this paper, we study the existence and uniqueness of coupled coincidence and common fixed points for single-valued and fuzzy mappings under contraction condition of rational type in b-metric space with a partial order and prove the existence of coupled coincidence and common fixed points for two single-valued mappings.

In this paper, some coupled coincidence and common xed point theorems for two self mappings have been derived which satisfy certain inequality involving a function of two variables that measures the distance between points in ordered metric spaces. For particular choices of the function several generalizations of many xed point theorems which contain altering distance functions may be obtained. Our results can be applied directly to study multidimensional xed point theorems which cover the concepts of coupled , tripled, quadruple xed point etc.

In this paper, we prove some xed point theorems in 2-Menger space under new contraction conditions.

In this paper we prove a common fixed point theorem for six compatible self mappings of type (A) in a complete non-Archimedean Menger PM-space.

In this paper, we show that some results of Sharma and Deshpande [19] are not valid, we also give supporting example. Finally, we consider the concept of weakly compatible mappings to improve the main result of Pathak [9].