Research Article Some Properties of Kantorovich-Stancu-Type Generalization of Szász Operators including Brenke-Type Polynomials via Power Series Summability Method Naim Latif Braha, 1,2 Toufik Mansour, 3 and Mohammad Mursaleen 4,5,6 1 Ilirias Research Institute, rr-Janina, No-2, Ferizaj 70000, Kosovo 2 Department of Mathematics and Computer Sciences, University of Prishtina, Avenue Mother Teresa, No-5, Prishtine 10000, Kosovo 3 Department of Mathematics, University of Haifa, 3498838 Haifa, Israel 4 Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan 5 Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India 6 Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan Correspondence should be addressed to Mohammad Mursaleen; mursaleenm@gmail.com Received 6 May 2020; Accepted 12 June 2020; Published 14 August 2020 Academic Editor: Lars E. Persson Copyright © 2020 Naim Latif Braha et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, we study the Kantorovich-Stancu-type generalization of Szász-Mirakyan operators including Brenke-type polynomials and prove a Korovkin-type theorem via the T -statistical convergence and power series summability method. Moreover, we determine the rate of the convergence. Furthermore, we establish the Voronovskaya- and Grüss-Voronovskaya- type theorems for T -statistical convergence. 1. Introduction and Preliminaries Let K ⊆ ℕ (set of natural numbers) and K m = fi ≤ m : i ∈ Kg. Then, the natural density or we can say asymptotic density of K is defined by σðKÞ = lim m ð1/mÞjK m j when- ever the limit exists, where jK m j denotes the cardinality of the set K m . A sequence η = ðη i Þ is statistically convergent to L if for every ε >0 lim m 1 m i ≤ m : η i − L j j ≥ ε f g j j = 0, ð1Þ and we write st − lim m η m = L. Let T = ðt nj Þ be a matrix and η = ðη j Þ be a sequence. The T − transform of the sequence η = ðη n Þ is defined by T η = ðT n ðηÞÞ, ðT ηÞ n = ∑ j t nj η j if the series converges for every n ∈ ℕ. We say that η is T − summable to the number L if ðT ηÞ n converges to L. The summability matrix T is regular whenever lim j η j = L = lim n ðT ηÞ n . Let T = ðt nj Þ be a regular matrix. A sequence η = ðη j Þ is said to be T -statistically convergent (see [1]) to real number L if for any >0, lim n ∑ j:jη j −Lj≥ε t nj =0, and we write st T − limη = L. If T is Cesàro matrix of order 1, then T -statistical convergence is reduced to the statistical convergence. In this paper, we also use the power series summability method which includes several known summability methods such as Abel and Borel (see [2–9]). Note that the power method is more effective than the ordinary convergence (see [10]). Let ðp j Þ be a sequence of real numbers such that p 0 >0, p 1 , p 2 , ⋯≥ 0, and the corresponding power series pðuÞ = ∑ ∞ j=0 p j u j has radius of convergence R with 0< R ≤∞. If lim u→R − ð1/pðuÞÞ∑ ∞ j=0 η j p j u j = L for all t ∈ ð0, RÞ, then we say that η = ðη j Þ is convergent in the sense of power series Hindawi Journal of Function Spaces Volume 2020, Article ID 3480607, 15 pages https://doi.org/10.1155/2020/3480607