Sequence Spaces Topics in Modern Summability Theory

This book is aimed at both experts and non-experts with an interest in getting acquainted with sequence spaces, matrix transformations and their applications. It consists of several new results which are part of the recent research on these topics. It provides different points of view in one volume, e.g. their topological properties, geometry and summability, fuzzy valued study and more. This book presents the important role sequences and series play in everyday life, it covers geometry of Banach Sequence Spaces, it discusses the importance of generalized limit, it offers spectrum and fine spectrum of several linear operators and includes fuzzy valued sequences which exhibits the study of sequence spaces in fuzzy settings. This book is the main attraction for those who work in Sequence Spaces, Summability Theory and would also serve as a good source of reference for those involved with any topic of Real or Functional Analysis.

1. Basic Functional Analysis. 2. Geometric Properties of Some Sequence Spaces. 3. Infinite Matrices. 4. Difference Sequence Spaces. 5. Almost Convergence and Classes of Related Matrix Transformations. 6. Spectrum of Some Triangle Matrices on Some Sequence Spaces. 7. Sets of Fuzzy Valued Sequences and Series.

Mohammad Mursaleen is presently a Principal Investigator for a SERB Core Research Grant at Department of Mathematics, Aligarh Muslim University. He has published more than 330 research papers in the field of Summability, Sequence Spaces, Approximation Theory, Fixed Point Theory, Measures of Noncompactness. He has also published 8 books and completed several National and International projects, visited several countries. Besides several master's students he has guided 20 Ph.D. students, and served as a reviewer for various international scientific journals. He is also amember of editorial boards of many international scientific journals.Feyzi Basar is a Professor Emeritus since July 2016, at ?In¨on¨u University,Turkey. He has published an e-book for graduate students and researchers and more than 150 scientific papers in the field of summability theory, sequence spaces, FK-spaces, Schauder bases, dual spaces, matrix transformations, spectrum of certain linear operators represented by a triangle matrix over some sequence space, the alpha-, beta- and gamma-duals and some topological properties of the domains of some double and four dimensional triangles in the certain spaces of single and double sequences, sets of the sequences of fuzzy numbers, multiplicative calculus. He has guided 17 master and 10 Ph.D. students., served as a referee for 121 international scientific journals. He is the member of editorial board of 21 scientific journals. Feyzi Basar is also a member of scientific committee of 17 mathematics conference, has given talks at 14 different universities as an invited speaker and participated in more than 70 mathematics symposium with a paper.