This paper introduces the Topkis-Veinott Multiobjective Optimization (TVMO) method for non linear constrained multiobjective problems (MOPs). TVMO extends the direction-based Topkis–Veinott ap proach from single-objective to multiobjective settings and, unlikescalarization methodswithpredefinedweights, is parameter-free and works directly with the vector of objectives. It handles infeasibility and constraint viola tions explicitly rather than through penalties. Each iteration solves an auxiliary quadratic subproblem to obtain a feasible improving direction, followed by a line search that selects the step length to maintain feasibility and ensure sufficient decrease of all objectives. Numerical experiments show that TVMO effectively approximates the nondominated front and outperforms some existing methods across multiple criteria, indicating strong reli ability for nonlinear constrained MOPs.
We prove some approximation results concerning the existence and uniqueness of the local solu tion of initial value problems of nonlinear Caputo fractional hybrid differential equations by using the monotone iteration method given by Dhage (2014) which is based on the recent hybrid fixed point principles. Next, an ap proximation result for Ulam-Hyers stability of the local solution of the considered equation is established and the monotonic dependence of the local solution on initial data is also discussed. Finally, a couple of examples are indicated to illustrate the hypotheses and abstract results of this paper
Inthispaper, we establish that any continuous mapping satisfying the condition of convex con traction with respect to the measure of noncompactness has at least one fixed point within a bounded, closed, and convex subset of a Banach space. Our results significantly generalize the Darbo fixed-point theorem. To demonstrate the applicability of these theoretical results, we present an existence theorem for the solution of a specific integral equation under certain conditions. Finally, we illustrate the practical use of the existence theorem with a concrete example
Let V be a vector space over a field F and U a fixed subspace of V. Define the set L_{GL(U)(V)} of all linear transformations on V whose restrictions to U are elements of the general linear group GL(U). Then L_{GL(U)(V)} is a regular subsemigroup of the full linear transformation semigroup L(V) under composition. In this paper, we characterize left (right) regular elements in L_{GL(U)(V)}, and determine when L_{GL(U)(V)} is a left (right) regular semigroup. We also provide a complete description of unit regular elements in L_{GL(U)(V)} and determine when L_{GL(U)(V)} is a unit regular semigroup. Moreover, the number of these elements is computed whenV is finite-dimensional and F is a finite field. Finally, we classify all maximal subsemigroups of L_{GL(U)(V)} and describe its maximal regular subsemigroups
In this paper, we investigate a generalized equilibrium problem for multivalued mappings de fined on the product of a convex subset of a topological vector space and an arbitrary nonempty set. Several existence results are established even when the underlying set is arbitrary and carries no specific algebraic or topological structure. Furthermore, we demonstrate that the sufficient conditions ensuring the existence of a solution can be imposed on a self-segment-dense subset rather than on the entire feasible set. The theoretical results are then applied to variational relation problems, vector equilibrium problems, and common fixed point problems, thereby unifying and extending a variety of known existence theorems in the literature.
