Iranian Journal of Science & Technology, Transaction A, Vol. 30, No. A2 Printed in The Islamic Republic of Iran, 2006  Shiraz University ON STRONGLY -SUMMABLE SEQUENCE SPACES * A. ESI ** AND H. POLAT Adiyaman University, Science and Art Faculty in Adiyaman, 02040, Adiyaman, Turkey Emails: aesi23@hotmail.com and hpolat@inonu.edu.tr Abstract ｱ In the present paper we define strongly -summable sequences which generalize A-summable sequences and prove such spaces to be complete paranormed spaces under certain conditions, some topological results have also been discussed. .e\ZorGs ｱ Difference sequence, paranorm 1. INTRODUCTION Let and be the Banach spaces of bounded, convergent and null sequences respectively, normed by . The notion of difference sequence space was introduced by Kizmaz [1] as follows: for , or where for all . Later, the difference sequence spaces were generalized by Et and dolak [2] as follows: Let be fixed, then for , or , where , and so . They showed that the above spaces are Banach spaces, normed by . Recently, difference sequence spaces have been discussed in Esi [3, 4], Tripathy [5] and many others. Let be an infinite matrix of non-negative real numbers and be a sequence such that . We write if converges for each n. Maddox [6] define , Received by the editor February 13, 2005 and in final revised form April 25, 2006 Corresponding author