Some new theorems on limits of variation

Some Utility Theorems on Inductive Limits of Preordered Topological Spaces

One of the main problems in utility theory is to find conditions which imply the numerical representability of topological spaces on which a preorder, or partial order, is defined. This study has reached a wide development in the literature: see, for instance, the works of Eilenberg, Debreu, Fleischer and Jaffray on completely preordered topological spaces [9, 7, 10, 15], and the seminal book b...

Some new localization theorems on Hamiltonian properties

Let G be a 2-connected graph with n ?: 3 vertices such that for any two vertices u, v at distance two in an induced subgraph K 1,3 or P4 of G, the inequality d(u) + d(v) ?: IN(u) U N(v) U N(w)ls holds for all w E N(u) n N(v). We prove that (i) if s = 1 and IN(u) n N(v)1 ?: 2, then G is hamiltonian or K p,p+1 ~ G ~ Kp + K p+1; (ii) if s = 0, then G is either pancyclic, or bipartite graph. This g...

Some New Generalizations of Karapinar’s Theorems

In-depth study of fixed point theory is to solve the existence of the equation Tx = x (or x ∈ T (x)), where T is a self-map or a non-self-map. However, as we know, the equation Tx = x (or x ∈ T (x)) is not necessarily to have a solution. So, we turn to explore the best approximation of the existence of solutions. In 2003, Kirk-Srinavasan-Veeramani [1] introduced cyclic maps and best proximity p...

Some Structure Theorems for Inverse Limits with Set-valued Functions

We investigate inverse limits with set-valued bonding functions. We generalize theorems of W. T. Ingram and William S. Mahavier, and of Van Nall, on the connectedness of the inverse limit space. We establish a fixed point theorem and show that under certain conditions, inverse limits with set-valued bonding functions can be realized as ordinary inverse limits. We also obtain some results that a...

Some Theorems on Coverings