H.M. Srivastava, Bidu Bhusan Jena, Susanta Kumar Paikray, Priyadarsini Parida, Deferred Cesàro Fibonacci statistical convergence and Korovkin-type approximation theorems

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DOI: 10.23952/jnva.10.2026.5.02

Volume 10, Issue 5, 1 October 2026, Pages 895-911

Abstract. In this paper, we introduce and investigate the notions of deferred Cesàro statistical convergence and deferred Cesàro Fibonacci statistical convergence within the framework of real sequence spaces, by establishing an inclusion relation between these two notions. Upon building on these foundations, we prove a new Korovkin-type approximation theorem for sequences of positive linear operators acting on trigonometric polynomials in $\mathfrak{C}_{2\pi}(\mathbb{R})$ , where convergence is considered in the sense of deferred Cesàro statistical convergence generated by Fibonacci sequences. The proposed theorem is shown to provide a genuine extension of several previously known Korovkin-type approximation results. Furthermore, we investigate the rate of deferred Cesàro Fibonacci statistical convergence for the same class of $2\pi$ -periodic functions. Finally, we show how the theoretical findings are supported by some illustrative examples that highlight the scope and applicability of the proposed approach in approximation theory.

How to Cite this Article:
H.M. Srivastava, B.B. Jena, S.K. Paikray, P. Parida, Deferred Cesàro Fibonacci statistical convergence and Korovkin-type approximation theorems, J. Nonlinear Var. Anal. 10 (2026), 895-911.