Mikail Et

In this work, new sequence spaces are introduced via the recently formulated Bell matrix, their Köthe–Toeplitz duals are determined, and a corresponding Schauder basis is established. In addition, various operator classes acting on these spaces are examined.

In this study, we give a neutrosophic statistical analysis of the meteorological elements (temperature, rainfall, and pressure) associated with major earthquakes that occurred in Türkiye between 2003 and 2023 by using meteorological data recorded (temperature, rainfall, and pressure) at the time of occurrence and 30 days before the earthquake in the cities. Neutrosophic results were compared with outcomes derived using classical statistical methods. The software developed within the scope of this study is designed as a neutrosophic regression‐based exploratory analysis tool that examines the statistical association between meteorological data and earthquake magnitude under uncertainty.

In this paper, we use the q -Fibonacci band matrix F ^ q = ( F ^ n ⁢ k ⁢ ( q ) ) {\widehat{F}_{q}=(\widehat{F}_{nk}(q))} to introduce the notions of q -Fibonacci summability, q -Fibonacci statistical convergence, strongly F ^ q ⁢ [ p ] {\widehat{F}_{q}[p]} -Cesàro summability and give some inclusion relations about these concepts.

In this paper, we further develop the study of the interplay between statistical and strong Cesàro convergence modulated by a modulus function, as initiated in the papers by Saavedra et al. and Romero de la Rosa. Our focus is on the deferred versions of these convergence methods. We show that the fundamental relationship between them remains valid in the deferred context, thereby extending and refining the results obtained by Bhardwaj and Gupta, and Belen and Yıldırım.

In this study, we construct a new triangular q?analogue of the q?Fibonacci matrix f?q =(fnk(q)) defined by fnk(q) = {qk fk(q)/f0n+2(q)?1, 1 ? k ? n, otherwise. After, we use the analogue to define the sequence spaces c( f?q), c0( f?q), ??( f?q), ?p( f?q) (1 ? p < ?). Then, we provide some inclusion relations for these spaces and examine a few topological characteristics. Furthermore, we construct a basis for the space ?p( f?q), calculate ??, ??, ??duals of the same space, characterize certain matrix classes, and look at some geometric properties.

In this presented article, we have exemplified and studied the Fr?chet differentiation of nonlinear operators between neutrosophic normed spaces as a generalization of notions given [34] and introduced nonlinear theory of neutrosophic bounded operators by introducing chain rule and some algebraic properties of Fr?chet differentiation of operators between neutrosophic normed spaces.