and Applied Analysis 3 2. Proof of Theorem 1 We need the following lemmas for the proof of Theorem 1. The difference analogue of the logarithmic derivative lemma was given by Halburd-Korhonen [8, Corollary 2.2] and Chiang-Feng [7, Corollary 2.6], independently. The following Lemma 8 is a variant of [8, Corollary 2.2]. Lemma 8. Let f(z) be a nonconstant meromorphic function of finite order, and ...

We investigate the problem of approximating function f in power-type weighted variable exponent Sobolev space Wr,p(.) ?(.) (0,1), (r = 1, 2, ...), by Hardy averaging operator A (f) (x) 1/x ?x0 f(t)dt. If lies ?(.)(0, 1), it is shown that A||(f)?f|| p(.),?(.)?rp(.) ? C ||f(r) p(.),?(.) , where a positive constant. Moreover, we consider boundedness grand Lebesgue spaces Lp(.),? ?(.)(0,1). The suf...

T h i s paper i s concerned w i t h a p l a n n i n g system f o r a r o b o t w i t h a hand and an eye w h i c h can m a n i p u l a t e b l o c k s . Two d i f f e r e n t k i n d s o f p r o b l e m s o l v e r s a r e used . One i s m a i n l y composed of a theorem p r o v e r based on t h e r e s o l u t i o n p r i n c i p l e , and the o t h e r c o n s i s t s o f a theorem p r o v e ...