In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η-convex function. Moreover, our results include several new and known results as special cases.

This paper aims to unify q-derivative/q-integral and h-derivative/h-integral in a single definition, this will be called q−h-derivative/q−h-integral. These notions are further extended on finite interval [a,b] in the form of left and right q−h-derivatives and q−h-integrals. Some inequalities are studied for q−h-integrals which are directly connected with well known results. In diverse fields of science and engineering the theory based on q-derivatives/q-integrals and h-derivatives/h-integrals can be unified by using the concept of q−h-derivative/q−h-integral.

Vertical graphene nanowalls (VGNWs) have emerged as a highly promising material in recent years due to their exceptional properties, such as a high specific surface area, excellent electrical conductivity, scalability, and compatibility with transition metal compounds. These attributes make VGNWs a compelling candidate for various applications, including energy storage, catalysis, and sensing, fostering great interest in their use in next future commercial graphene-based sensors like optoelectronic and plasmonic devices, energy storage electrodes, and catalytic systems. Among the diverse graphene synthesis methods, plasma-enhanced chemical vapor deposition (PECVD) has proven to be a robust technique for producing large-scale graphene films and creating VGNWs on diverse substrates. However, despite substantial progress in optimizing growth conditions to achieve micrometer-sized graphene nanowalls, the outcomes are often obtained through empirical approaches, and a comprehensive understanding of the underlying physicochemical mechanisms governing nanostructure formation remains elusive. In particular, a deeper exploration of atomic-level phenomena, such as nucleation, carbon precursor adsorption, and surface diffusion of adatoms, is imperative to exert precise control over the growth process. Concerning the synthesis of VGNWs, hydrogen plays a dual role in the graphene growth process, acting as both a co-catalyst and an etchant for the nanowalls. Nevertheless, a thorough comprehension of the intricate growth process is still required. To address these knowledge gaps, this review paper aims to investigate the nucleation and growth of VGNWs using PECVD, with a specific focus on exploring the temperature effect on the graphene growth ratio and nucleation density across a wide range of temperatures. By providing valuable insights into the PECVD process, our objective is to enable the optimization of growth conditions for tailoring VGNWs' properties, thereby facilitating their application in energy storage, catalysis, and sensing fields.