In 2018, Erdal Karapinar introduced the concept of interpolative Kannan operators, a novel adaptation of the Kannan mapping originally defined in 1969 by Kannan. This new mapping condition is more lenient than the basic contraction condition. In this paper, we study the concept by introducing the IKC-iterated function/multi-function system using interpolative Kannan operators, including a broader area of mappings. Moreover, we establish the Collage Theorem endowed with the iterated function system (IFS) based on the IKC, and show the well-posedness of the IKC-IFS. Interpolative Kannan contractions are meaningful due to their applications in fractals, offering a more versatile framework for creating intricate geometric structures with potentially fewer constraints compared to classical approaches.

Cross nanofluid possesses an extraordinary quality among the various fluidic models to explore the key characteristics of flowing fluid during very low and very high shear rates and its viscosity models depend upon shear rate. The current study establishes the numerical treatment regarding variable viscosity-based mixed convective inclined magnetized Cross nanofluid with varying thermal conductivities over the moving permeable surface. Along with variable thermal conductivities, we considered thermal radiation, thermophoresis, and the Brownian motion effect. An inclined magnetic field was launched for velocity scrutiny and the heat transfer fact was numerically seen by mixed convective conditions. Similarity variables were actioned on generated PDEs of the physical model and conversion was performed into ODEs. Numerical results showed that the frictional force and Nusselt quantity considerably influence the skinning heat transfer processes over the geometry of a moving permeable surface. Furthermore, less velocity was noticed for the greater suction parameter and the Brownian motion parameter corresponds to lower mass transport.

This article focuses on a numerical investigation aimed at enhancing the electrical performance of a two-dimensional photovoltaic thermal system (PV/T) through the application of cooling using hybrid nanofluids. The hybrid nanofluids consist of titanium oxide and silver nanoparticles suspended in water, while the PV/T system is based on polycrystalline silicon, copper, and a flow channel with a rotating cylinder. PV/T devices generate electricity from sunlight, but their performance degrades over time due to the heat generated by solar radiation. Therefore, nanofluids can be circulated through the bottom flow channel to cool the device. This study utilizes 2D incompressible Navier–Stokes equations to control fluid flow and energy equations to manage energy distribution. The COMSOL 6.0 finite element software is employed for comprehensive modeling and simulation. To enhance the performance of the PV/T system, a parametric study is conducted by varying the Reynolds number (ranging from 100 to 1000), cylinder rotational speed (varying from 0.01 to 0.2 m s⁻¹), and silver volume fraction (ranging from 0.01 to 0.2). The results show that increasing the Reynolds number and the volume fraction of silver leads to a reduction in the maximum temperature of the cell. The maximum temperature of the cell also decreases with the rotational speed of the cylinder but only for high Reynolds numbers. By applying the present model, the cell's efficiency is improved by 5.93%.

This article is aimed at introducing an iterative scheme to approximate the common solution of split variational inclusion and a fixed-point problem of a finite collection of nonexpansive mappings. It is proven that under some suitable assumptions, the sequences achieved by the proposed iterative scheme converge strongly to a common element of the solution sets of these problems. Some consequences of the main theorem are also given. Finally, the convergence analysis of the sequences achieved from the iterative scheme is illustrated with the help of a numerical example.