The Nepali Mathematical Sciences Report, Vol.38, No.1, 2021: 31-38 DOI: https://doi.org/10.3126/nmsr.v38i1.38901 INDEXED ABSOLUTE CES ` ARO SUMMABILITY FOR INFINITE SERIES SMITA SONKER 1 , ALKA MUNJAL 2 , LAKSHMI NARAYAN MISHRA 3,* 1 Department of Mathematics, National Institute of Technology Kurukshetra, Kurukshetra-136119, India smita.sonker@gmail.com 2 Department of Mathematics, Akal University Talwandi Sabo-151302, Bathinda, India alka math@auts.ac.in 3 Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Bathinda, India lakshminarayanmishra04@gmail.com Abstract: In the present study, a wider class of sequence is used for a least set of sufficient conditions for absolute Ces` aro ϕ -|C, α, β; δ; γ| k summable factor for an infinite series. Many corollaries have been deter- mined by using sutaible conditions in the main theorem. Validation of the theorem done by the previous findings of summablity. In this way, system’s stability is improved by finding the conditions for absolute summability. Key Words: Abel’s transformation, Absolute Ces`aro Summability, H¨ older’s inequality, Minkowski’s in- equality AMS (MOS) Subject Classification. 40F05, 40D20, 40G05. Received: March 7, 2021 Accepted: June 6, 2021 Published Online: June 31, 2021 1. Introduction Let partial sums’ sequence of ∑ a n is given by s n = ∑ n k=0 a k and n th sequence to sequence transform of the sequence {s n } is determined by u n , s.t., (1.1) u n = ∞  k=0 u nk s k An infinite series ∑ a n is absolutely summable, if (1.2) lim i→∞ u i = s