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ON ESTIMATION OF UNIFORM CONVERGENCE OF ANALYTIC FUNCTIONS BY (p, q)-BERNSTEIN OPERATORS
Mursaleen, M.,Khan, Faisal,Saif, Mohd,Khan, Abdul Hakim The Kangwon-Kyungki Mathematical Society 2019 한국수학논문집 Vol.27 No.2
In this paper we study the approximation properties of a continuous function by the sequence of (p, q)-Bernstein operators for q > p > 1. We obtain bounds of (p, q)-Bernstein operators. Further we prove that if a continuous function admits an analytic continuation into the disk $\{z:{\mid}z{\mid}{\leq}{\rho}\}$, then $B^n_{p,q}(g;z){\rightarrow}g(z)(n{\rightarrow}{\infty})$ uniformly on any compact set in the given disk $\{z:{\mid}z{\mid}{\leq}{\rho}\}$, ${\rho}>0$.
M. Mursaleen,Sunil K. Sharma,Qamaruddin 강원경기수학회 2021 한국수학논문집 Vol.29 No.2
In the present paper we introduce some sequence spaces over $n$-normed spaces defined by fractional difference operator and Musielak-Orlicz function $\mathcal{M} = (\mathfrak{F}_i)$. We also study some topological properties and prove some inclusion relations between these spaces.
STATISTICAL A-SUMMABILITY OF DOUBLE SEQUENCES AND A KOROVKIN TYPE APPROXIMATION THEOREM
Belen, Cemal,Mursaleen, Mohammad,Yildirim, Mustafa Korean Mathematical Society 2012 대한수학회보 Vol.49 No.4
In this paper, we define the notion of statistical A-summability for double sequences and find its relation with A-statistical convergence. We apply our new method of summability to prove a Korovkin-type approximation theorem for a function of two variables. Furthermore, through an example, it is shown that our theorem is stronger than classical and statistical cases.
COMPACT MATRIX OPERATORS BETWEEN THE SPACES m(ϕ), n(ϕ) AND ℓ<sub>p</sub>
Malkowsky, Eberhard,Mursaleen, Mohammad Korean Mathematical Society 2011 대한수학회보 Vol.48 No.5
We give the characterizations of the classes of matrix trans-formations ($m(\phi),{\ell}_p$), ($n(\phi),{\ell}_p$) ([5, Theorem 2]), (${\ell}_p,m(\phi)$) ([5, Theorem 1]) and (${\ell}_p,n(\phi)$) for $1{\leq}p{\leq}{\infty}$, establish estimates for the norms of the bounded linear operators defined by those matrix transformations and characterize the corresponding subclasses of compact matrix operators.
Compact matrix operators between the spaces m(Ø), n(Ø) and l_p
Eberhard Malkowsky,Mohammad Mursaleen 대한수학회 2011 대한수학회보 Vol.48 No.5
We give the characterizations of the classes of matrix transformations (m(Ø),l_p), (n(Ø),l_p) ([5, Theorem 2]), (l_p, m(Ø)) ([5, Theorem 1]) and (l_p,n(Ø)) for 1≤ p≤ ∞, establish estimates for the norms of the bounded linear operators defined by those matrix transformations, and characterize the corresponding subclasses of compact matrix operators.
STATISTICAL A-SUMMABILITY OF DOUBLE SEQUENCES AND A KOROVKIN TYPE APPROXIMATION THEOREM
Cemal Belen,Mohammad Mursaleen,Mustafa Yildirim 대한수학회 2012 대한수학회보 Vol.49 No.4
In this paper, we dene the notion of statistical A-summabil-ity for double sequences and nd its relation with A-statistical conver-gence. We apply our new method of summability to prove a Korovkin-type approximation theorem for a function of two variables. Furthermore,through an example, it is shown
Taimur, Sadaf,Onuki, Motoharu,Mursaleen, Huma 서울대학교 교육연구소 2022 Asia Pacific Education Review Vol.23 No.4
The current research explores the transformative potential of Design Thinking (DT) pedagogy in Higher Sustainability Education (HSE) in a hybrid (mix of online and face-to-face) setting. The case study examined a Field Exercise in Sustainability Science (FESS) course, using DT pedagogy, in a HSE program at a university in Japan. The critical transformative learning experiences (i.e., signs of transformative learning) were captured to investigate whether DT pedagogy has allowed learners to challenge their perspectives and go through the transformative learning experience. The qualitative case study captures the critical transformative learning experiences by collecting students’ perspectives through semi-structured interviews, reflections, and class observations. As a result, the research successfully captured the signs of transformative learning, where each student went through multidimensional and embodied transformative experiences. Furthermore, the results show how DT as a pedagogy can support transformative learning in HSE by encouraging disorienting dilemmas, promoting reflection and discourse, fostering relationships, providing context, and offering an engaging experience. DT as a pedagogy can bring transformative learning into practice in HSE, and it can be implemented effectively using a digital or hybrid learning approach without a need for complex structural changes. The paper can provide concrete lessons for practice and curriculum development to bring transformative learning into digital teaching practice in HSE.