ISSN: 2455-7749

**
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).

**References**

Bor, H. (1993). On absolute summability factors. Proceedings of the American Mathematical Society, 118(1), 71-75.

Bor, H. (2011a). An application of almost increasing sequences, Applied Mathematical Letters, 24(3), 298-301.

Bor, H. (2011b). Factors for generalized absolute Cesàro summability. Mathematical and Computer Modelling, 53(5-6), 1150-1153.

Bor, H. (2014). Almost increasing sequences and their new applications II, Filomat, 28(3) 435-439.

Bor, H. (2015). Some new results on infinite series and Fourier series, Positivity, 19(3), 467-473.

Bor, H. (2016). Generalized absolute Cesàro summability factors, Bulletin of Mathematical Analysis and Applications, 8(1), 6-10.

Chandra, P., & Jain, H.C. (1988). Absolute product summability of the Fourier series and its allied series, Communications, Faculty of Science, University of Ankara Series A1, 37, 95-107.

Chauhan, V., & Srivastava, P.K. (2019). Computational techniques based on runge-kutta method of various order and type for solving differential equations, International Journal of Mathematical, Engineering and Management Sciences, 4(2), 375–386.

Flett, T.M. (1957). On an extension of absolute summability and some theorems of Littlewood and Paley. Proceedings of the London Mathematical Society, 3(1), 113-141.

Leindler, L. (2001). A new application of quasi power increasing sequences. Publicationes Mathematicae, 58(4), 791-796.

Özarslan, H.S., & Ari, T. (2011). Absolute matrix summability methods. Applied Mathematics Letters, 24(12), 2102-2106.

Özarslan, H.S., & Yavuz, E. (2013). A new note on absolute matrix summability, J. Inequalities and Applications, 2013:474, 1-7.

Parashar, V.K. (1981). On (N, Pn) and (K, 1, α) summability methods, Publications de L'Institut Mathèmatique Nouvelle Série, 29(43), 145-158.

Richa, & Kumar, A. (2019). Dominant pole based approximation for discrete time system, International Journal of Mathematical, Engineering and Management Sciences, 4(1), 56–65.

Singh, U.P., Medhavi, A., Gupta, R.S., & Bhatt, S.S. (2018). Theoretical study of heat transfer on peristaltic transport of non-newtonian fluid flowing in a channel: Rabinowitsch fluid model. International Journal of Mathematical, Engineering and Management Sciences, 3(4), 450–471.

Sonker, S., & Munjal, A. (2016a). Absolute summability factor φ-〖|C,1; δ|〗_k of infinite series, International Journal of Mathematical Analysis, 10(23), 1129-1136.

Sonker, S., & Munjal, A. (2016b). Sufficient conditions for triple matrices to be bounded, Nonlinear Studies, 23(4), 533-542.

Sonker, S., & Munjal, A. (2017). Absolute φ-〖|C,α,β;δ|〗_k summability of Infinite series, Journal of Inequalities and Applications, 168, 1-7.

Sulaiman, W.T. (2006). Extension on absolute summability factors of infinite series. Journal of Mathematical Analysis and Applications, 322(2), 1224-1230.