On $ f $-strongly Cesàro and $ f $-statistical derivable functions

Bilal Altay; Francisco Javier García-Pacheco; Ramazan Kama; Bilal Altay; Francisco Javier García-Pacheco; Ramazan Kama

doi:10.3934/math.2022629

AIMS Mathematics

2022, Volume 7, Issue 6: 11276-11291. doi: 10.3934/math.2022629

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On $ f $-strongly Cesàro and $ f $-statistical derivable functions

Bilal Altay ¹,
Francisco Javier García-Pacheco ^{2
,
,},
Ramazan Kama ³

1.
Department of Mathematics and Physical Sciences Education, Faculty of Education, İnönü University, 44280 Malatya, Turkey
2.
Department of Mathematics, College of Engineering, University of Cadiz, Avda. de la Universidad de Cádiz 10, Puerto Real 11519, Spain (EU)
3.
Department of Mathematics and Physical Sciences Education, Faculty of Education, Siirt University, The Kezer Campus, Kezer, 56100 Siirt, Turkey

Received: 10 December 2021 Revised: 09 February 2022 Accepted: 16 February 2022 Published: 11 April 2022
MSC : 16W80, 46H25, 54H13

In this manuscript, we introduce the following novel concepts for real functions related to $ f $-convergence and $ f $-statistical convergence: $ f $-statistical continuity, $ f $-statistical derivative, and $ f $-strongly Cesàro derivative. In the first subsection of original results, the $ f $-statistical continuity is related to continuity. In the second subsection, the $ f $-statistical derivative is related to the derivative. In the third and final subsection of results, the $ f $-strongly Cesàro derivative is related to the strongly Cesàro derivative and to the $ f $-statistical derivative. Under suitable conditions of the modulus $ f $, several characterizations involving the previous concepts have been obtained.
- statistical convergence,
- $ f $-statistical convergence,
- Cesàro convergence,
- strongly Cesàro convergence,
- discrete derivative
Citation: Bilal Altay, Francisco Javier García-Pacheco, Ramazan Kama. On $ f $-strongly Cesàro and $ f $-statistical derivable functions[J]. AIMS Mathematics, 2022, 7(6): 11276-11291. doi: 10.3934/math.2022629

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Abstract

In this manuscript, we introduce the following novel concepts for real functions related to $ f $-convergence and $ f $-statistical convergence: $ f $-statistical continuity, $ f $-statistical derivative, and $ f $-strongly Cesàro derivative. In the first subsection of original results, the $ f $-statistical continuity is related to continuity. In the second subsection, the $ f $-statistical derivative is related to the derivative. In the third and final subsection of results, the $ f $-strongly Cesàro derivative is related to the strongly Cesàro derivative and to the $ f $-statistical derivative. Under suitable conditions of the modulus $ f $, several characterizations involving the previous concepts have been obtained.

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