In this work, we study the lacunary I -statistical convergence concept of complex uncertain triple sequence. Four types of lacunary I -statistically convergent complex uncertain triple sequences are presented, namely lacunary I -statistical convergence in measure, in mean, in distribution and with respect to almost surely, and some basic properties are proved.
The study aimed to determine the characteristics of pre-service teachers’ 21st-century skill concepts and their compatibility with the contemporary 21st-century skill lists, 21st-century self-skills and to compare and discuss, in terms of curricula and their fields. 71 pre-service science and 59 pre-service mathematics teachers were participated this phenomenological study. The statements by the participants were transformed into codes. These codes were categorized based on the framework for the 21st century skills. 21st-century skills codes with contemporary concepts relating to subcategories like “cognitive skills”, “process skills”, “communication and collaboration skills”, “initiative and self-direction skills”, “career skills”, and “technology knowledge/usage/production skills” indicate that teacher candidates are knowledgeable about 21st-century skills. Also the study found out that the greatest effects on the 21st-century skills of pre-service science and mathematics teachers are the curricula and the education they are taught. In this context, this research was based on the belief that determining the influence of pre-service teachers’ out-of-school and in-school trainings, their curricula, branches, etc. on their 21st-century skills will be guiding in terms of organizing curricula and environments of education.
Fast [12] is credited with pioneering the field of statistical convergence. This topic has been researched in many spaces such as topological spaces, cone metric spaces, and so on (see, for example [19, 21]). A cone metric space was proposed by Huang and Zhang [17]. The primary distinction between a cone metric and a metric is that a cone metric is valued in an ordered Banach space. Li et al. [21] investigated the definitions of statistical convergence and statistical boundedness of a sequence in a cone metric space. Recently, Sakaoğlu and Yurdakadim [29] have introduced the concepts of quasi-statistical convergence. The notion of quasi I-statistical convergence for triple and multiple index sequences in cone metric spaces on topological vector spaces is introduced in this study, and we also examine certain theorems connected to quasi I-statistically convergent multiple sequences. Finally, we will provide some findings based on these theorems.
Nanda [29] 1989 yılında bütün yakınsak bulanık sayı dizilerinin tam metrik uzaylar olduğunu gösterdi. Ayrıca, Nuray [30] bulanık sayılarda lacunary istatistiksel yakınsak ve istatistiksel yakınsak diziler arasındaki ilişkileri verdi. Bununla birlikte, bulanık sayı dizilerinin çeşitli yönleri birçok yazar tarafından tartışılmıştır. Bu çalışmada, üç indisli bir bulanık sayı dizisinin lacunary istatistiksel yakınsaklığı ve üç indisli lacunary güçlü p-Cesàro toplanabilmesi kavramları incelenmiştir. Üç indisli lacunary istatistiksel Cauchy dizisi, üç indisli lacunary güçlü p-Cesàro toplanabilme ve lacunary istatistiksel olarak bulanık bir sayıya yakınsak olmayı tanımlıyoruz. Bu çeşitli kavramlar arasında bir ilişki olduğunu düşünüyoruz ve bu nedenle, makalede bu konu ile ilgili bazı temel teoremlere yer veriyoruz.
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