On q-statistical convergence and statistical solution of q-Cauchy problem

Zengin G. G., Kalita H., SAVAŞ E., Dutta T. K.

Filomat, vol.40, no.3, pp.865-879, 2026 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 3
  • Publication Date: 2026
  • Doi Number: 10.2298/fil2603865g
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.865-879
  • Keywords: Cauchy Probelm, q-integrable function, q-statistical convergence, q-statistically Cauchy, stastical solutions
  • Uşak University Affiliated: Yes

Abstract

In this paper, we present the concept of q-statistical convergence for any sequence of real-valued functions. Several characteristics of q-statistical convergence for sequences of functions with real values are examined. Further, we introduce the notion of q-statistical convergence for sequences of Jackson integrable functions. Finally, we determine the q-statistical solution of q-differential equations that involve non-uniquely solvable Cauchy problems.