# Orhan TuğTishk International University · Mathematics Education

Orhan Tuğ

Doctor of Philosophy

## About

39

Publications

5,428

Reads

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154

Citations

Citations since 2017

Introduction

I got my Ph.D. degree at University of Nis, under the supervision of Serbian mathematician professor Vladimir Rakocevic. My research area falls into but not limited to Mathematical and Functional Analysis. I generally study on summability theory for both single and double sequences, matrix methods, dual spaces, matrix transformations, operator theory, spectral theory on sequence spaces, measure theory, and measure of non compactness of bounded operators.

Additional affiliations

September 2011 - present

**Tishk International University**

Position

- Head of Department

Education

September 2017 - July 2019

## Publications

Publications (39)

Most recently, some new double sequence spaces B(Mu), B(Cϑ) where ϑ={b,bp,r,f,f0} and B(Lq) for 0<q<∞ have been introduced as the domain of four-dimensional generalized difference matrix B(r,s,t,u) in the double sequence spaces Mu, Cϑ where ϑ={b,bp,r,f,f0} and Lq for 0<q<∞, and some topological properties, dual spaces, some new four-dimensional mat...

We consider the generalised Hahn sequence space \(h_{d}\), where d is an unbounded monotone increasing sequence of positive real numbers, and characterise several classes of bounded linear operators or matrix transformations from \(h_{d}\) into the spaces of all bounded, convergent and null sequences, and into the space of all abolutely convergent...

In this paper, we define the third order generalized difference operator \(\Delta _i^3\), where $$\begin{aligned} (\Delta _i^3x)_k=\sum _{i=0}^3\frac{(-1)^i}{i+1}\left( {\begin{array}{c}3\\ i\end{array}}\right) x_{k-i}= x_k-\frac{3}{2}x_{k-1}+x_{k-2}-\frac{1}{4}x_{k-3}, \end{aligned}$$and show that it is a linear bounded operator on the Hahn sequen...

Most recently, the generalized difference operator Δ 3 i of order three was defined and its domain in Hahn sequence space h was calculated. In this paper, the spaces ℓ 1 (Δ 3 i) and bv(Δ 3 i) are introduced as the domain of generalized difference operator Δ 3 i of order three in the sequence spaces ℓ 1 and bv. en, some topological properties of ℓ 1...

Dear Academicians,
We are pleased to announce that registration for the 9th ICOWOBASS-2023 conference is officially open.
The 9th ICOWOBAS-2023, International Conference and Workshop on Basic and Applied Sciences, is a biannual conference organized by four worldwide universities, Tishk International University(Iraq), Salahaddin University Erbil (Ir...

In this paper, the spaces 1(Δ3
i ) and bv(Δ3
i ) are introduced as the domain of generalized difference operator Δ3
i of order
three in the sequence spaces 1 and bv. Then, some topological properties of 1(Δ3
i ) and bv(Δ3
i ) are given, and some inclusion
relations are shown. Additionally, α−, β− and γ−dual spaces of 1(Δ3
i ) and bv(Δ3
i ) are comp...

Let h d = f = (f k) ∈ ω : k d k | f k − f k+1 | < ∞ ∩ c 0 , where d = (d k) is an unbounded and monotonic increasing sequence of positive reals. We study the matrix domains h d (C q) = (h d) C q and bv(C q) = (bv) C q , where C q is the q-Cesàro matrix, 0 < q < 1. Apart from the inclusion relations and Schauder basis, we compute α-, β-and γ-duals o...

In this paper, first we define a matrix operator A = (a nk ) by
an,k={ 1/2(k=n, n-1)~(n=0,1,2….) 0 otherwise,
and we show that A = (a nk ) is a linear and bounded operator on Hahn sequence space h. Then we calculate the fine spectrum of matrix operator A = (a nk ) on the Hahn sequence space h. We also determine the point spectrum, the residual spe...

In this article, we define the new generalized Hahn sequence space h d p , where d = d k k = 1 ∞ is monotonically increasing sequence with d k ≠ 0 for all k ∈ ℕ , and 1 < p < ∞ . Then, we prove some topological properties and calculate the α − , β − , and γ − duals of h d p . Furthermore, we characterize the new matrix classes h d , λ , where λ = b...

The Department of Mathematics Education at Tishk International University invites you to an International Workshop titled, 1st International Workshop on Global Contributions to Mathematical Sciences; themed “Operator theory and its interdisciplinary applications.”
The workshop on Global Contributions to Mathematical Sciences is the maiden internat...

The ICASEE-2022 conference with its broad spectrum of themes and branches covered, plans for embracing sustainable environment and cleaner energy through applied science research. The event targets to present new insights to values and standards of environmental protection, future trends of progression mechanisms of improvement, harder trials of di...

In order to enable the knowledge and information accessible to everyone, Faculty of Education, Tishk International University is to hold the annual International Conference on Applied Sciences, Energy and Environment. The ICASEE-2022 conference is designed to attract the research communities to promote connections between theory and practice and ex...

In this paper, we introduce the new spaces [Formula: see text] of double sequences of bounded variation, where [Formula: see text], and we investigate some topological properties. Moreover, we prove some strict inclusion relations and we examine [Formula: see text]-dual of the spaces [Formula: see text]. Finally, we characterize some classes of fou...

Tishk International University organizes an international conference, ICASEE-2022 and we would like to invite all academics, experts, field workers to participate in our conference. The accepted papers will be published in ARO- Scientific journal of Koya University (https://aro.koyauniversity.org/index.php/aro) which is a WoS journal indexed in ESC...

In this paper, we define some new almost and strongly almost convergent double sequence spaces B ̃(C_f), B ̃(C_f0), B ̃[C_f] and B ̃[C_f0] derived by the domain of four-dimensional sequential band matrix B(r ̃,s ̃,t ̃,u ̃) in the spaces C_f, C_f0 , [C_f] and [C_f0 ], respectively. Then we study some topological properties and prove some strict incl...

In this paper, we introduce some new double sequence spaces $\mathcal{M}_u(\Delta)$ and $\mathcal{C}_{\vartheta}(\Delta)$, where $\vartheta\in\{bp,bp0,r,r0\}$ as the domains of the four-dimensional forward difference matrix in the double sequence spaces $\mathcal{M}_u$ and $\mathcal{C}_{\vartheta}$, respectively. Then we investigate some topologica...

Let E represent any of the spaces M u , C ϑ ( ϑ = { b , b p , r } ) , and L q ( 0 < q < ∞ ) of bounded, ϑ -convergent, and q-absolutely summable double sequences, respectively, and E ˜ be the domain of the four-dimensional (4D) infinite sequential band matrix B ( r ˜ , s ˜ , t ˜ , u ˜ ) in the double sequence space E, where r ˜ = ( r m ) m = 0 ∞ ,...

In this dissertation, some new double sequence spaces derived as the domain of the four-dimensional generalized difference matrix are investigated. In the first chapter; literature review and some needed definitions and theorems are given for the following chapters. In the second chapter; we investigate the double sequence and series spaces with th...

Most recently, some new double sequence spaces $B(\mathcal{M}_{u})$, $B(\mathcal{C}_{\vartheta})$ where $\vartheta=\{b,bp,r,f,f_0\}$ and $B(\mathcal{L}_{q})$ for $0<q<\infty$ have been introduced as four-dimensional generalized difference matrix $B(r,s,t,u)$ domain on the double sequence spaces $\mathcal{M}_{u}$, $\mathcal{C}_{\vartheta}$ where $\v...

We firstly summarize the related literature about Br,s,t,u -summability of double sequence spaces and almost Br,s,t,u -summable double sequence spaces. Then we characterize some new matrix classes of Ls′:Cf , BLs′:Cf , and Ls′:BCf of four-dimensional matrices in both cases of 0<s′≤1 and 1<s′<∞ , and we complete this work with some significant resul...

Theconceptofafour-dimensionalgeneralizeddiﬀerencematrixanditsdomainon somedoublesequencespaceswasrecentlyintroducedandstudiedbyTu˘gandBa¸sar (AIPConferenceProceedings,vol.1759,2016)andTu˘g(J.Inequal.Appl.2017(1):149, 2017).Inthispresentpaper,asanaturalcontinuationof(J.Inequal.Appl.2017(1):149, 2017),weintroducenewalmostnullandalmostconvergentdouble...

Tuǧ and Başar [3] have recently studied the concept of four dimensional generalized difference matrix B(r, s, t, u) and its matrix domain in some double sequence spaces. In this present paper, as a natural continuation of [3], we introduce new almost null and almost convergent double sequence spaces\(B(C_f)\) and \(B(C_{f_0})\) as the domain of fou...

In this paper, we introduce a new sequence space bv(Nt) as the domain of Nörlund matrix Nt in the space of all sequences of bounded variation. Firstly, we give some topological properties and inclusion relations. Moreover, we determine the α-, β- and γ- duals of the space bv(Nt) . Finally, we characterize some new matrix classes over the space bv(N...

In this paper, I introduce a new sequence space as the domain of four dimensional
generalized difference matrix and as a generalization of the series space . I give some
topological properties with some inclusion relations. Moreover, I calculate beta(bp)- and gamma- duals
of the new sequence space . In the last section I characterize some matrix...

In this paper, we make a literature review on p-adic sequences and we prove some new topological properties on the sequence spaces w(p), l∞(p) and c(p) of p-adic numbers as the set of all sequences, the set of bounded sequences and the set of convergent sequences of p-adic numbers, respectively. We show that these sequence spaces are Banach spaces...

In this study, I introduce some new double sequence spaces B(Mu), B(Cp), B(Cbp), B(Cr)
and B(Lq) as the domain of four-dimensional generalized difference matrix B(r,s,t, u)
in the spaces Mu, Cp, Cbp, Cr and Lq, respectively. I show that the double sequence
spaces B(Mu), B(Cbp) and B(Cr) are the Banach spaces under some certain conditions.
I give so...

In this paper, some new Ideal convergent sequence spaces and that are related to the summability method, are introduced and some topological properties of these spaces and some inclusion relations and results are determined.

In this study, we introduce some new double sequence spaces B(M u ), B(C p ), B(C bp ), B(C r ) and B(L q ) as the domain of four-dimensional generalized difference matrix B(r,s,t,u) in the spaces M u , C p , C bp , C r and L q , respectively. We show that the double sequence spaces B(M u ), B(C bp ) and B(C r ) are the Banach spaces under some cer...

In this article, the sequence spaces f0(Nt) and f (Nt) are introduced as the domain of Nörlund mean in the spaces f0 and f of almost null and almost convergent sequences which are isomorphic to the spaces f0 and f, respectively, and some inclusion relations are given. Additionally, alpha, beta and gamma duals of the sequence spaces f0(Nt) and f (Nt...

In this article, the sequence spaces c 0 (N t) and c(N t) are introduced as the domain of Nörlund mean N t in the spaces c0 and c of null and convergent sequences which are isomorphic to the spaces c0 and c, respectively, and some inclusion relations are given. Additionally, Schauder basis for the spaces c0(N t) and c(N t) are constructed and their...

In this article, the sequence spaces c 0 (N t) and c(N t) are introduced as the domain of Nörlund mean N t in the spaces c0 and c of null and convergent sequences which are isomorphic to the spaces c0 and c, respectively, and some inclusion relations are given. Additionally, Schauder basis for the spaces c0(N t) and c(N t) are constructed and their...

We generalize some sequence spaces from single to double, we study some topological properties of these double sequence spaces by using ideal convergence, difference sequence spaces, and an Orlicz function in 2-normed spaces, and we give some results related to these sequence spaces.

Das and Patel (1989) introduced two new sequence spaces which are called lacunary almost convergent and lacunary strongly almost convergent sequence spaces. Móricz and Rhoades (1988) defined and studied almost P-convergent double sequences spaces. Savaş and Patterson (2005) introduce the almost lacunary strong P-convergent double sequence spaces by...

## Questions

Questions (9)

The story of publishing papers in journals is twofold; before and after Covid-19. I have this classification because when I compare the APCs of journals before and after Covid-19, I see that there is a big increment. But, there is another option, submitting the paper to the special issues with very low APCs. Right here I have these questions. What is the difference between publishing papers on special issues and regular issues? What are the advantages of getting published in the special issues? What is the reliability of getting published in the special issues?

Every higher education institution has its publication award/ incentive system. Some use the Quartile category, some Clarivate Analytics. But the application differs from university to university. I have also seen Impact Factor base calculation of incentive payment for academic publication in some universities. My request here is that could you please share the publication award system that you use in your institution? The thing is that there are many methods to calculate it, but we don't know which one is much more systematic and beneficial for our institution, too. Thanks in advance for answering my question.

We plan to establish a new international mathematics and statistics journal. The purpose is to publish original research papers as well as review works. We have a very strong team in the region to be able to struggle with the editing, reviewing and publishing issues.

we would like to hear some experienced people about the difficulties and the steps that we should follow at the very beginning. Also, we would like to ask about the possibility, process, and requirements of establishing this journal under well-known publishing houses like Hindawi, Springer, Elsevier,...

Thanks in advance for your kind reply.

As you know that some journals are asking you to submit your paper to ArXiv first and they evaluate your paper later. But if that journal reject your paper you are not able to delete or cancel the record on ArXiv. Then if you want to submit this same paper to another journal, then you face problem with overlapping with that ArXiv record. So how can we solve this problem and how can we publish our paper which is submitted to the arXiv before?

Before starting to the question, I wish get rid of the corona virus infection disease for all humanity. Nowadays we are all indirectly effected by this virus and we are not able to teach on campus. Now we are looking for a way to be able to teach online. But as you know that we need at least a board and stuff to teach as theoretical advanced math instructor. I need your valuable ideas and offers like platforms that we teach through. Thanks in advance for your valuable answers.

while looking for an internationally job, the best way is to google by writing the job imagine of us to the search button. But unfortunately we are unable to reach easily to the best fitting job. The question is where and how should we look for the best fitting and international job offers in order to be applied online?

## Projects

Projects (6)

ICNAA 2022 (https://conferences.dbuniversity.ac.in/icnaa2022/) aims to bring together leading academicians, researchers and research scholars to interchange and share their knowledge, experiences and research results on various aspects of nonlinear science and its applications in different fields. It also comes up with an interdisciplinary stage for scientists, researchers, and inventors to present and discuss the latest innovations and trends in the field of Engineering, Physics and Applied Mathematics. Please see the details at https://conferences.dbuniversity.ac.in/icnaa2022/

The aim of this project is to create some new results for double sequence spaces which are much more general than the results which were done by four-dimensional difference matrix and four-dimensional generalized difference matrix.

By this project, we aimed to fill the gap in the literature which are the direct open problems and consequences after the works"Tuğ, O., 2018. On almost B-summable double sequence spaces. Journal of inequalities and applications, 2018(1), p.9." and "Orhan Tug, “On the Characterization of Some Classes of Four-Dimensional Matrices and Almost -Summable Double Sequences,” Journal of Mathematics, vol. 2018, Article ID 1826485, 7 pages, 2018. https://doi.org/10.1155/2018/1826485."