We prove a vector-valued version of Muić's integral non-vanishing criterion for Poincaré series on the upper half-plane H. Moreover, we give an accompanying result construction modular forms in form series. As application these results, construct and study classical elliptic

Fourier analysis is a powerful tool for many problems, and especially for solving various differential equations of interest in science and engineering. In the present paper since the utilization of Zadeh's Extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct a fuzzy-valued function on a closed interval via related membership function. We de...

Given any Banach space X, let L X 2 denote the Banach space of all measurable functions f : [0, 1] → X for which f 2 := 1 0 f (t) 2 dt