Topics in Contemporary Mathematical Analysis and Applications

6 On Indexed Product Summability of an Infinite Series

B. P. Padhy

KIIT Deemed to be University

P. Baliarsingh

Gangadhar Meher University

CONTENTS

6.1     Introduction

6.1.1     Historical Background

6.1.2     Notations and Definitions

6.2     Known Results

6.3     Main Results

6.4     Proof of Main Results

6.5     Conclusion

References

6.1     Introduction

6.1.1     Historical Background

Initially, in 1952, Szasz [10] published some results on products of summability methods. Subsequently, Rajgopal [7] in 1954, Parameswaran [6] in 1957, Ramanujan [8] in 1958, etc. published some more results on the products of summability methods. Later on, Das [2] in 1969 proved some related results on the absolute product summability. In 2008, Sulaiman ...