Applied Summability Methods
Published on 10. April 2014
Book
Paperback/Softback
X, 124 pages
978-3-319-04608-2 (ISBN)
Description
This short monograph is the first book to focus exclusively on the study of summability methods, which have become active areas of research in recent years. The book provides basic definitions of sequence spaces, matrix transformations, regular matrices and some special matrices, making the material accessible to mathematicians who are new to the subject. Among the core items covered are the proof of the Prime Number Theorem using Lambert's summability and Wiener's Tauberian theorem, some results on summability tests for singular points of an analytic function, and analytic continuation through Lototski summability. Almost summability is introduced to prove Korovkin-type approximation theorems and the last chapters feature statistical summability, statistical approximation, and some applications of summability methods in fixed point theorems.
More details
Series
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Research
Illustrations
X, 124 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 8 mm
Weight
219 gr
ISBN-13
978-3-319-04608-2 (9783319046082)
DOI
10.1007/978-3-319-04609-9
Schweitzer Classification
Other editions
Additional editions
M. Mursaleen
Applied Summability Methods
E-Book
03/2014
1st Edition
Springer
€53.49
Available for download
Person
M. MURSALEEN is a full professor of Mathematics at Aligarh Muslim University, Aligarh. Earlier, he worked as a full professor of Mathematics at King Abdulaziz University, Jeddah, Saudi Arabia, during 2004-2006. An active researcher, Prof. Mursaleen has authored two books and five book chapters, in addition to his contributions to 190 research papers to various international journals such as Proc. Amer. Math. Soc., Quarterly J. Math. (Oxford), Studia Math., Information Sciences, and Chaos, Solitons & Fractals to name a few. Prof. Mursaleen is reviewer for Mathematical Reviews (USA) since 1982, as well as referee of about 100 scientific journals (most of them are SCI/SCI expended journals). He has also guided 12 PhD students so far. He has visited about 16 countries including USA & UK and delivered about 32 talks, He has also participated in joint research work with faculty members of the host institutions. Prof. Mursaleen is member of the editorial board of various scientific journals and has served as member of various international scientific bodies and organizing committees that include International Council of Scientists "Global World Communicator Education and Science". He has worked on a number of joint projects of international collaboration. His main research interests are Sequence Spaces, Summability Theory, Approximation Theory, Functional Equations, Measures of Non-compactness and Fixed-Point Theory.
S.A. MOHIUDDINE is associate professor of Mathematics at King Abdulaziz University, Jeddah, Saudi Arabia. He received his PhD degree from Aligarh Muslim University, Aligarh, India. He was awarded postdoctoral fellowship by National Board for Higher Mathematics (NBHM), Department of Atomic Energy, Government of India. His main research interests are field of sequences spaces, measures of noncompactness, approximation theory, summability theory and fixed point theory. Prof. Mohiuddine has publishedover 70 research papers in several international journals and 2 book chapters. He is reviewer for Mathematical Reviews (USA) and referee for many scientific journals. He is also member of the editorial board of some mathematical journals.
Content
Toeplitz Matrices.- Lambert Summability and the Prime Number Theorem.- Summability Tests for Singular Points.- Lototski Summability and Analytic Continuation.- Summability Methods for Random Variables.- Almost Summability.- Almost Summability of Taylor Series.- Matrix Summability of Fourier and Walsh-Fourier Series.- Almost Convergence in Approximation Process.- Statistical Summability.- Statistical Approximation.- Applications to fixed point theorems.- Bibliography.- Index.