konuralp j. math. Konuralp Journal of Mathematics 2147-625X Mehmet Zeki SARIKAYA Approximation Theory and Asymptotic Methods Yaklaşım Teorisi ve Asimptotik Yöntemler $q$-Cesaro Summable Sequences Defined by Orlicz Function Tabassum Sabiha Zakir Hussain College Kumar Praveen Aligarh Muslim University Esi Ayhan Malatya Turgut Ozal University 04 30 2026 14 1 135 141 10 07 2025 01 16 2026 Copyright © 2013, Konuralp Journal of Mathematics 2013 Konuralp Journal of Mathematics

This paper introduces and systematically investigates the sequence spaces defined by the combination of q-calculus, statistical convergence, and Orlicz functions. We begin by defining the concept of q-statistical convergence with respect to an Orlicz function M, denoted by SMq . Furthermore, we introduce the notion of q-strong summability w.r.t an Orlicz function M, denoted by WMq . We establish several inclusion relations between the spaces SMq and WMq and other classical sequence spaces. We prove that, under suitable conditions, both SMq and WMq are linear spaces.

 q-calculus statistical convergence strong summability Orlicz function [1] Mohammad Mursaleen, Sabiha Tabassum, and Ruqaiyya Fatma. On the q-statistical convergence of double sequences. Periodica Mathematica Hungarica, 88(2):324, 334, 2024. [2] J. Connor, On strong matrix summability with respect to a modulus and statistical convergence. Canad. Math. Bull. 32 (2) (1989), 194–198. [3] H. Fast. Sur la convergence statistique. Colloquium Mathematicae, 2(3-4):241, 244, 1951. [4] H. Steinhaus. Sur la convergence ordinaire et la convergence asymptotique. Colloquium Mathematicae, 2(1):73, 74, 1951. [5] M Mursaleen, Sabiha Tabassum, and Ruqaiyya Fatma. On q-statistical summability method and its properties. Iranian Journal of Science and Technology, Transactions A: Science, 46(2):455 ,460, 2022. [6] T. ˇ Sal´at, “On statistically convergent sequences of real numbers.” Mathematica Slovaca, 30(2) (1980), 139–150. [7] J. Connor, The statistical and strong p-cesaro convergence of sequences. Analysis, 8(1-2)(1988), 47–64. [8] O. Duman, “Generalized Ces`aro summability of Fourier series and its applications.” Constructive Mathematical Analysis, 4(2) (2021), 135–144. [9] A. Zygmund, Trigonometric series. Cambridge University Press, 1959. [10] I. S. Ibrahim and R. C¸ olak, “On the sets of f -strongly Ces`aro summable sequences.” Kyungpook Mathematical Journal, 64 (2024), 235–244. [11] A. Esi and M. Et. Some new sequence spaces defined by a sequence of Orlicz functions. Indian J.Pure Appl. Math. 3198 (2000) 967-972. [12] J. Lindenstrauss and L. Tzafiri, On Orlicz sequence spaces. Israel J. Math. 10(1971) 379-390. [13] A. Aizpuru, M. Listan-Garcia, and F. Rambla-Barreno. Density by moduli and statistical convergence. Quaest. Math., 37(4)(2014), 525-530. [14] V. K. Bhardwaj and S. Dhawan. “ f -statistical convergence of order a and strong Ces`aro summability of order a with respect to a modulus.” Journal of Inequalities and Applications, 2015:67 (2015), 1–14. [15] I.J. Maddox. Sequence spaces defined by modulus. Math. Proc. Comb. Soc. 100(1986), 161-166. [16] E. Savas¸ and R. Savas¸. “Some sequence spaces defined by Orlicz functions.” Archivum Mathematicum, 40(1) (2004), 33–40. [17] F. Nuray, U. Ulusu and E. D¨undar. “Ces`aro summability of double sequences of sets”. General Mathematical Notes, 25(1) (2014), 8–18. [18] F. Nuray, E. D¨undar and U. Ulusu, “Deferred strongly Ces`aro summable and statistically convergent functions”. Honam Mathematical Journal, 44(4) (2022), 560–571. [19] U. Ulusu and E. G¨ulle, “On double Wijsman strong deferred Ces`aro summable set sequences”. Facta Universitatis, Series: Mathematics and Informatics, 40(2) (2025), 333–341.