the notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  probabilistic metric space was  introduced by karl menger. alsina, schweizer and sklar gave a general definition of  probabilistic normed space based on the definition of menger [1]. in this note we study the pn spaces which are  topological vector spaces and the open mapping an...

In this paper, a numerical method is proposed for solving optimal control problem of Volterra integral equations using radial basis functions (RBFs) for approximating unknown function. Actually, the method is based on interpolation by radial basis functions including multiquadrics (MQs), to determine the control vector and the corresponding state vector in linear dynamic system while minimizing...

for all f ∈ Cb(R ) and λ is continuous in the sense that if {fj} ∞ j=1 is a sequence of bounded continuous functions on R which is uniformly bounded and converges uniformly on compact subsets of R to a bounded continuous function f , then {λ(fj)} ∞ j=1 converges to λ(f). If f is any bounded continuous function on R, then there is a sequence {fj} ∞ j=1 of continuous functions on R n such that ea...

Quality Growth Index (QGI) is affected by two sets of combined-structural and social indicators. Structural indicator contributes to achieve the main target of sound-sustainable-competitive output growth. By the way, the sound output growth should enhance social-public services and living standards. Although QGIs are weightedly computed based on different scenarios, the trend of the QGIs and co...

Abstract The paper alluded to in the title contains following striking result: Let $I$ be unit interval and $\Delta$ Cantor set. If $X$ is a quasi Banach space containing no copy of $c_{0}$ which isomorphic closed subspace with basis $C(I,\,X)$ linearly homeomorphic $C(\Delta ,\, X)$ , then locally convex, i.e., space. We will show that Kalton result sharp by exhibiting non-locally convex space...