Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO)

From KKM Class to KC Class of Multimaps

2024-04-22T11:48:15+07:00

This is to give a short history of our multimap classes $\mathfrak{K,\ KC,\ KO}$ in the KKM theory. We show that many authors adopted or imitated the inadequate definition of the KKM class due to Chang and Yen in 1996. We list such works in chronological order and also introduce other works which extended the class properly. Our study on such history will improve the KKM theory in the new millennium.

Homoclinic Transition to Chaos in the Duffing Oscillator Driven by Periodic Piecewise Linear Forces

2024-04-22T11:55:39+07:00

We have applied the Melnikov criterion to examine a homoclinic bifurcation and transition to chaos in the Duffing oscillator driven by different forms of periodic piecewise linear forces. The periodic piecewise linear forces considered are triangular, hat, trapezium, quadratic and rectangular types of forces. For all the forces, an analytical threshold condition for the homoclinic transition to chaos is derived using Melnikov method and Melnikov threshold curves are drawn in a parameter space. Using the Melnikov threshold curves, we have found a critical forcing amplitude fc above which the system may behave chaotically. We have analyzed both analytically and numerically the homoclinic transition to chaos in the Duffing system with เธฎเธ•-parametric force also. The predictions from Melnikov method have been further verified numerically by integrating the governing equation and finding areas of chaotic behaviour.

A Three Layer Supply Chain Coordination Policies for Price Sensitive and Exponentially Declining Demand with Recommended Retail Price by Manufacturer

2024-04-22T12:00:54+07:00

The article develops an integrated supply chain coordination for multi-channel and multi-echelon supply, in which a single manufacturer, multiple non-competitive distributors, and non-competitive retailers are work together as members of the supply chain. The formulation of this model is based on deterministic exponential decreasing and price-dependent demand on the retailer's end. We formulated the model in two different scenarios, first, one is decentralized,d and the second one is centralized. The integrated profit function has been derived for each supply chain member, incorporating sharing holding costs among the distributors and retailers. We optimized selling price, economical order quantity, wholesale price, and profits for every echelon supply chain member in the finite and certain time horizon for decentralized and centralized scenarios respectively. Finally, we have done sensitivity analysis for some key parameters to examine their influence on the model's outputs. On the basis of numerical studies, we have also proposed managerial insights.

On Existence of Solution of Implicit Vector Equilibrium Problems for Trifunction

2024-04-22T12:05:22+07:00

In this work, we introduce and study an extended version of implicit vector equilibrium problems for trifunction in real Hausdorff topological vector spaces. We prove some new existence results for the solution of these problems by using KKM lemma in real Hausdorff topological vector spaces. Some special cases are also discussed.