International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749

Sufficient Conditions for Absolute Cesàro Summable Factor

Smita Sonker
Department of Mathematics, National Institute of Technology, Kurukshetra-136119, India.

Alka Munjal
Department of Mathematics, National Institute of Technology, Kurukshetra-136119, India.

DOI https://dx.doi.org/10.33889/IJMEMS.2019.4.3-050

Received on May 31, 2018
  ;
Accepted on February 27, 2019

Abstract

Quasi-f-power increasing sequence has been used for infinite series to establish a theorem on a minimal set of sufficient conditions for absolute Cesàro φ-|〖C,α;δ;l|〗_k summable factor. Further, a set of new and well-known arbitrary results have been obtained by using the main theorem. The presented main result has been validated by the previous result under suitable conditions. In this way, the Bounded Input Bounded Output (BIBO) stability of impulse response has been improved by finding a minimal set of sufficient conditions for absolute summability because absolute summable is the necessary and sufficient condition for BIBO stability.

Keywords- Absolute summability, Cesaro summability, Infinite series, Quasi-f-power increasing sequence.

Citation

Sonker, S., & Munjal, A. (2019). Sufficient Conditions for Absolute Cesàro Summable Factor. International Journal of Mathematical, Engineering and Management Sciences, 4(3), 627-634. https://dx.doi.org/10.33889/IJMEMS.2019.4.3-050.

Conflict of Interest

The authors declare that there is no conflict of interest for this publication.

Acknowledgements

The authors express their sincere gratitude to the Department of Science and Technology (India) for providing the financial support to the second author under INSPIRE Scheme (Innovation in Science Pursuit for Inspired Research Scheme).

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