Existence, uniqueness, Ulam–Hyers–Rassias stability, well-posedness and data dependence property related to a fixed point problem in gamma-complete metric spaces with application to integral equations

In this paper, we study a fixed point problem for certain rational contractions on γ-complete metric spaces. Uniqueness of the fixed point is obtained under additional conditions. The Ulam–Hyers–Rassias stability of the problem is investigated. Well-posedness of the problem and the data dependence property are also explored. There are several corollaries of the main result. Finally, our fixed point theorem is applied to solve a problem of integral equation. There is no continuity assumption on the mapping.

Forecasting Stochastic Volatility Characteristics for the Financial Fossil Oil Market Densities

This paper builds and implements multifactor stochastic volatility models for the international oil/energy markets (Brent oil and WTI oil) for the period 2011–2021. The main objective is to make step ahead volatility predictions for the front month contracts followed by an implication discussion for the market (differences) and observed data dependence important for market participants, implying predictability. The paper estimates multifactor stochastic volatility models for both contracts giving access to a long-simulated realization of the state vector with associated contract movements. The realization establishes a functional form of the conditional distributions, which are evaluated on observed data giving the conditional mean function for the volatility factors at the data points (nonlinear Kalman filter). For both Brent and WTI oil contracts, the first factor is a slow-moving persistent factor while the second factor is a fast-moving immediate mean reverting factor. The negative correlation between the mean and volatility suggests higher volatilities from negative price movements. The results indicate that holding volatility as an asset of its own is insurance against market crashes as well as being an excellent diversification instrument. Furthermore, the volatility data dependence is strong, indicating predictability. Hence, using the Kalman filter from a realization of an optimal multifactor SV model visualizes the latent step ahead volatility paths, and the data dependence gives access to accurate static forecasts. The results extend market transparency and make it easier to implement risk management including derivative trading (including swaps).

Zenali Iteration Method For Approximating Fixed Point of A δZA - Quasi Contractive mappings

This article will introduce a new iteration method called the zenali iteration method for the approximation of fixed points. We show that our iteration process is faster than the current leading iterations like Mann, Ishikawa, oor, D- iterations, and *- iteration for new contraction mappings called quasi contraction mappings. And we proved that all these iterations (Mann, Ishikawa, oor, D- iterations and *- iteration) equivalent to approximate fixed points of quasi contraction. We support our analytic proof by a numerical example, data dependence result for contraction mappings type by employing zenali iteration also discussed.

Fixed Point, Data Dependence, and Well-Posed Problems for Multivalued Nonlinear Contractions

The aim of the paper is to discuss data dependence, existence of fixed points, strict fixed points, and well posedness of some multivalued generalized contractions in the setting of complete metric spaces. Using auxiliary functions, we introduce Wardowski type multivalued nonlinear operators that satisfy a novel class of contractive requirements. Furthermore, the existence and data dependence findings for these multivalued operators are obtained. A nontrivial example is also provided to support the results. The results generalize, improve, and extend existing results in the literature.

Effects of mesh loop modes on performance of unstructured finite volume GPU simulations

In unstructured finite volume method, loop on different mesh components such as cells, faces, nodes, etc is used widely for the traversal of data. Mesh loop results in direct or indirect data access that affects data locality significantly. By loop on mesh, many threads accessing the same data lead to data dependence. Both data locality and data dependence play an important part in the performance of GPU simulations. For optimizing a GPU-accelerated unstructured finite volume Computational Fluid Dynamics (CFD) program, the performance of hot spots under different loops on cells, faces, and nodes is evaluated on Nvidia Tesla V100 and K80. Numerical tests under different mesh scales show that the effects of mesh loop modes are different on data locality and data dependence. Specifically, face loop makes the best data locality, so long as access to face data exists in kernels. Cell loop brings the smallest overheads due to non-coalescing data access, when both cell and node data are used in computing without face data. Cell loop owns the best performance in the condition that only indirect access of cell data exists in kernels. Atomic operations reduced the performance of kernels largely in K80, which is not obvious on V100. With the suitable mesh loop mode in all kernels, the overall performance of GPU simulations can be increased by 15%-20%. Finally, the program on a single GPU V100 can achieve maximum 21.7 and average 14.1 speed up compared with 28 MPI tasks on two Intel CPUs Xeon Gold 6132.

Effects of Mesh Loop Modes on Performance of Unstructured Finite Volume GPU Simulations

In unstructured finite volume method, loop on different mesh components such as cells, faces, nodes, etc is used widely for the traversal of data. Mesh loop results in direct or indirect data access that affects data locality significantly. By loop on mesh, many threads accessing the same data lead to data dependence. Both data locality and data dependence play an important part in the performance of GPU simulations. For optimizing a GPU-accelerated unstructured finite volume Computational Fluid Dynamics (CFD) program, the performance of hot spots under different loops on cells, faces, and nodes is evaluated on Nvidia Tesla V100 and K80. Numerical tests under different mesh scales show that the effects of mesh loop modes are different on data locality and data dependence. Specifically, face loop makes the best data locality, so long as access to face data exists in kernels. Cell loop brings the smallest overheads due to non-coalescing data access, when both cell and node data are used in computing without face data. Cell loop owns the best performance in the condition that only indirect access of cell data exists in kernels. Atomic operations reduced the performance of kernels largely in K80, which is not obvious on V100. With the suitable mesh loop mode in all kernels, the overall performance of GPU simulations can be increased by 15%-20%. Finally, the program on a single GPU V100 can achieve 4.8 speed up comparing with 28 MPI tasks on two Intel CPUs Xeon Gold 6132.