In the theory of optimization, in connection with ordinary and partial differential equations, a number of closure and lower closure theorems have been obtained in different contexts and under a variety of conditions and modes of convergence. In particular "seminormali ty" conditions (property (Q) and its variants) have played different roles. In this paper we first prove closure and lower clos...

Abstract In this paper we introduce some new types of contractive mappings by combining Caristi contraction, ?iri?-quasi contraction and weak in the framework a metric space. We prove fixed point theorems for such type over complete spaces with help ? -diminishing property. Some examples are given strengthening hypothesis our established theorems.

The main goal of this paper is to present comparison theorems proven under natural conditions such as N2 ≥ N1 and M−1 1 ≥ M−1 2 for weak and weaker splittings of A = M1 − N1 = M2 − N2 in the cases when A−1 ≥ 0 and A−1 ≤ 0.

We discuss the following viscosity approximations with the weak contraction A for a nonexpansive mapping sequence {Tn}, yn αnAyn 1 − αn Tnyn, xn 1 αnAxn 1 − αn Tnxn. We prove that Browder’s and Halpern’s type convergence theorems imply Moudafi’s viscosity approximations with the weak contraction, and give the estimate of convergence rate between Halpern’s type iteration and Mouda’s viscosity ap...

The objective of this paper is to deal with the fuzzy conic programming problems. The aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. Toward this end, The convexity-like concept of fuzzy mappings is introduced and then a specific ordering cone is established based on the parameterized representation of fuzzy numbers. Under this setting, duality theo...

The weak ergodic theorems of mathematical demography state that the age distribution of a closed population is asymptotically independent of the initial distribution. In this paper, we provide a new proof of the weak ergodic theorem of the multistate population model with continuous time. The main tool to attain this purpose is a theory of multiplicative processes, which was mainly developed by...

The main purpose of this paper is to give weak and strong convergence theorems of a new three-step iterative scheme for asymptotically nonexpansive mappings in Banach spaces and we also give several weak and strong convergence theorems of the three-step iterative scheme with errors for asymptotically nonexpansive mappings in Banach spaces. Mann-type and Ishikawa -type iterations are included by...

Given a weakly uniformly globally asymptotically stable closed (not necessarily compact) set A for a differential inclusion that is defined on Rn, is locally Lipschitz on Rn\A, and satisfies other basic conditions, we construct a weak Lyapunov function that is locally Lipschitz on Rn. Using this result, we show that uniform global asymptotic controllability to a closed (not necessarily compact)...