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Öğe ALMOST CONVERGENCE AND DOUBLE SEQUENTIAL BAND MATRIX(Springer, 2014) Candan, MuratThe class f of almost convergent sequences was introduced by G.G. Lorentz, using the idea of the Banach limits [A contribution to the theory of divergent sequences, Acta Math. 80(1948), 167-190]. Let f(0) ((B) over tilde) and f((B) over tilde) be the domain of the double sequential band matrix (B) over tilde((r) over tilde, (s) over tilde) in the sequence spaces f(0) and f. In this article, the beta- and gamma-duals of the space f(/3) are determined. Additionally, we give some inclusion theorems concerning with the spaces f(0)((B) over tilde) and f((B) over tilde). Moreover, the classes (f ((B) over tilde) :,mu,) and (mu : f((B) over tilde)) of infinite matrices are characterized, and the characterizations of some other classes are also given as an application of those main results, where mu is an arbitrary sequence space.Öğe A different approach for almost sequence spaces defined by a generalized weighted means(Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2017) Kılınç, Gülsen; Candan, MuratÖz: In this study, we introduce (, ), (, ) and (, ) sequence spaces which consisting of all the sequences whose generalized weighted -difference means are found in , and spaces utilising generalized weighted mean and -difference matrices. The -and the -duals of the spaces (, ) and (, ) are determined. At the same time, we have characterized the infinite matrices ((, ): ) and (: (, )), where is any given sequence space.Öğe Domain of the double sequential band matrix in the classical sequence spaces(Springeropen, 2012) Candan, MuratLet. denote any one of the classical spaces iota(infinity), c, c(0) and iota(p) of bounded, convergent, null and absolutely p- summable sequences, respectively, and lambda also be the domain of the double sequential band matrix B(r,s) in the sequence space lambda, where (r(n))(infinity)(n = 0) and (s(n))(infinity) (n = 0) are given convergent sequences of positive real numbers and 1 <= pÖğe Domain of the double sequential band matrix in the spaces of convergent and null sequences(Springer, 2014) Candan, MuratWhat stands out in this article is the sequence spaces of a new brand c(0)(lambda)((B) over tilde) and c(lambda)((B) over tilde), derived by using a double sequential band matrix B(T-,'s-) which generalizes the previous work of Sonmez and Baar (Abstr. Appl. Anal. 2012:435076,2012), where (r(n))(n=0)(infinity) and (s(n))(n=0)(infinity) are given convergent sequences of positive real numbers. The aforementioned spaces are in fact the BK-spaces of non-absolute type. Moreover, they are norm isomorphic to the spaces co and c, respectively. Then, some inclusion relations are derived to determine the alpha-, beta- and gamma-duals of these spaces. Next, their Schauder bases are constructed. In conclusion, some matrix classes from the spaces c(0)(lambda)((B) over tilde) and c(lambda)((B) over tilde) to the spaces l(p), C-o and c are characterized. When compared with the corresponding results in the literature, it is seen that the results of the present study are more general and more inclusive.Öğe Hemen Hemen Yakınsak Dizi Uzaylar için Yeni Bir Bakış(2018) Candan, MuratBanach limiti (Acta. Math. 80. 1948, 167-190) kavramını kullanarak G.G. Lorentz hemen hemen yakınsak dizilerin c^ uzayını tanımladı. Bu çalışmada öne çıkan nokta 0 c^ , c^ ve c^s uzaylarının Candan [2] tarafından tanımlanan R G B ~ . ~ = matris etki alanında olan B G c ~ 0^ , B Gc ~ ^ ve B G cs ~ ^ uzaylarını tanımlamaktır. Burada B ~ ikili dizisel band matrisi G de genelleştirilmiş ağırlıklı ortalamayı göstermektedir. Çalışmada öncelikle B G c ~ 0^ , B Gc ~ ^ ve B G cs ~ ^ uzaylarının sırası ile 0 c^ , c^ ve c^s uzaylarına lineer izomorf oldukları gösterildikten sonra B Gc ~ ^ ve B G cs ~ ^ uzaylarının sırası ile ? - ve ? - dualleri elde edilmiştir. Son bölümde de ? verilen herhangi bir dizi uzayı olmak üzere (^ :?) ~ B Gc ve ( ) B Gc ~ ? : ^ matris sınıflarının karekterizasyonu verilmiştir.Öğe A New Aspect for Some Sequence Spaces Derived Using the Domain of the Matrix $widehat{widehat{B}}$(2022) Candan, MuratThis study serves for analysing algebraic and topological characteristics of the sequence spaces $X(widehat{widehat{B}}(r,s))$ constituted by using non-zero real number $r$ and $s$, where $X$ denotes arbitrary of the classical sequence spaces $ell_{infty}, c, c_{0} $ and $ell_{p}$ $(1<p<infty)$ of bounded, convergent, null and absolutely $p$-summable sequences, respectively and $X(widehat{widehat{B}})$ also is the domain of the matrix $widehat{widehat{B}}(r,s)$ in the sequence space $X$. Briefly, the $beta$- and $gamma$-duals of the space $X(widehat{widehat{B}})$ are computed, and Schauder bases for the spaces $c(widehat{widehat{B}})$, $c_{0}(widehat{widehat{B}})$ and $ell_{p}(widehat{widehat{B}})$ are determined, and some algebraic and topological properties of the spaces $c_{0}(widehat{widehat{B}})$, $ell_{1}(widehat{widehat{B}})$ and $ell_{p}(widehat{widehat{B}})$ are studied. Additionally, it is observed that all these spaces have some remarkable features, including the classes $(X_{1}(widehat{widehat{B}})$: $X_{2})$ and $(X_{1}(widehat{widehat{B}}): X_{2}(widehat{widehat{B}}))$ of infinite matrices which are characterized, in which $X_{1}in{ ell_{infty},c,c_{0},ell_{p},ell_{1}}$ and $X_{2}in{ell_{infty},c,c_{0},ell_{1}}$.Öğe On traveling wave solutions for the transmission line model of nano-ionic currents along MTs arising in nanobiosciences(Springer, 2024) Juadih, Walla Rahim; Candan, Murat; Singh, Gurpreet; Eslami, Baharak; Manafian, Jalil; Kaur, Irwanjot; Alkader, Naief AlabedThis paper presents many new soliton solutions in equation of nano-ionic currents along microtubules using an improved tan(phi/2)-expansion method, the generalized (G '/G)-expansion technique and the Exp-function method. The abundant solutions including kink soliton solution, hyperbolic solution, trigonometric solution and bell-shaped soliton solutions are attained. Comparing our new results with the well-known results show that obtained solutions are the plenty types of three forms containing soliton, periodic and kink-singular solutions. The outcomes illustrate that the previously mentioned strategies are more effective than the Ansatz strategies as modified extended tanh-function applied by Sekulic et al. (Appl Math Comput 218:3499-3506, 2011) and solitary wave ansatz method applied by Younis and Ali (Appl Math Comput 246:460-463, 2014). The mentioned methods are very simple and concise and can be also applied to other nonlinear partial differential equations. More importantly, the solutions found in this work can have significant applications in microtubules systems where solitons are used to nano-ionic structures.Öğe Operators on some vector-valued Orlicz sequence spaces(Fırat Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, 2005) Yılmaz, Yılmaz; Özdemir, M. Kemal; Solak, İhsan; Candan, MuratÖz: Bu çalışmada, bazı vektör-değerli Orlicz dizi uzayları için bir baz ile aynı işleve sahip olan bir operatör dizisi tanımladık. Ayrıca, bundan faydalanarak hM(X) uzayından ? uzayına sürekli operatörlerin Extra open brace or missing close brace uzayını karakterize ettik. Burada M bir Orlicz fonksiyonu, X, ? Banach uzayları ve hM(X), ?k=1xM(xk?)0 için olacak şekildeki tüm X-değerli x=(xk) dizilerinin uzayıdır. Aslında, tam olarak, bazı şartlar altında, her bir T?B(hM(X),Y) operatörünün Ak?B(X,?) operatörlerinin bir A=(Ak)xk=1 dizisine denk olduğu sonucuna ulaştık. 2000 Matematik Konu Sınıflaması: 46A45,47A05,47A67,46A20.Öğe Özel fonksiyonlar yardımıyla tanımlanmış bazı yeni dizi uzayları(İnönü Üniversitesi, 2006) Candan, MuratBeş bülümden meydana gelen bu şalışmada, (X, q) yarınormlu uzayı uzerinde f s ou cs ü Ë Ë modülüs ve M Orlicz fonksiyonları kullanılarak w A, p, f, q, s , w A, p, M, q, s , uu Ë Ë w â r , A, p, M, q, s ve w â r , A, p, f, q, s dizi uzayları tanımları verildi. Birinci bülümde, ileriki bülümlerde kullanılacak olan temel kavramlar ve ou ou Fonksiyonel Analizin bazı ünemli araşları yer almaktadır. o c Ë Ikinci bülümde, ilk olarak modülüs fonksiyonunun şalışmamızda kullandığımız ou uu cs g Ë p, f, q, s bazı ozelikleri verildi. Daha sonra (X, q)'nun tam olması durumunda w0 A, ü nin tam paranormlu uzay olduğu güsterilerek bazı kapsama bağıntıları verildi. Son go g Ë olarakta w A, p, f v , q, s dizi uzayı oluşturulup, v, m â N nin durumlarına güre s o Ë Ë w A, p, f v , q, s ve w A, p, f m , q, s dizi uzayları arasındaki bağıntılar incelendi. g ü cü u o u u Uşuncü bülümün ilk kısmında, M.A. Krasnosel'skii & Y.B. Rutickii'nin ve daha sonraları M.M. Rao & Z.D. Ren'in ayrıntılı olarak incelediği, konveks fonksiyonların g üzel bir sınıfında yer alan Orlicz fonksiyonlarının bazı üzelikleri sunuldu. o o Dürdüncü bülümde r â N, â xk = xk â xk+1 , â r xk = â râ 1 xk â â râ 1 xk+1 , o u u ou Ë Ë ve M Orlicz fonksiyonu olmak uzere w0 â r , A, p, M, q, s , w â r , A, p, M, q, s , ü Ë wâ â r , A, p, M, q, s genelleştirilmiş fark dizi uzayları tanımlanıp, bu uzayların s s bazı üzelikleri incelenmiştir. o s i Son bülümde r â N, â xk = xk â xk+1 , â r xk = â râ 1 xk â â râ 1 xk+1 , ve f ou Ë Ë modülüs fonksiyonu olmak uzere w0 â r , A, p, f, q, s , w â r , A, p, f, q, s , uu ü Ë wâ â r , A, p, f, q, s genelleştirilmiş fark dizi uzayları tanımlanıp, bu uzayların bazı s s üzelikleri incelenmiştir. o s Ë ANAHTAR KELIMELER: Dizi uzayı, Modülüs fonksiyonu, Orlicz fonksiyonu, uu paranormlu uzay, fark dizi uzayı.Öğe Paranormed Sequence Space of Non-absolute Type Founded Using Generalized Difference Matrix(Natl Acad Sciences India, 2015) Candan, Murat; Gunes, AsumanThe present paper introduces the generalized Riesz difference sequence space r(q)(B-u(p)) that consists of all sequences whose (RuB)-B-q-transforms are in the space l(p), where B stands for generalized difference matrix. Some topological properties of the new brand sequence space have been investigated as well as alpha- beta- and gamma-duals. In addition to this, we have also constructed the basis of r(q)(B-u(p)). At the end of the article, we characterize a matrix class on the sequence space. These results are more general and more comprehensive than the corresponding results in the literature.Öğe A Robust Approach About Compact Operators on Some Generalized Fibonacci Difference Sequence Spaces(2024) Candan, MuratIn this new study, which deals with the different properties of ?p( ?F (r, s)) (1 ? p < ?) and ??( ?F (r, s)) spaces defined by Candan and Kara in 2015 by using Fibonacci numbers according to a certain rule, we have tried to review all the qualities and features that the authors of the previous editions have found most useful. This document provides everything needed to characterize the matrix class (?1, ?p( ?F (r, s))) (1 ? p < ?) . Using the Hausdorff measure of non-compactness, we simultaneously provide estimates for the norms of the bounded linear operators LA defined by these matrix transformations and identify requirements to derive the corresponding subclasses of compact matrix operators. The results of the current research can be regarded as to be more inclusive and broader when compared to the similar results available in the literature.Öğe Some Characteristics of Matrix Operators on Generalized Fibonacci Weighted Difference Sequence Space(Mdpi, 2022) Candan, MuratThe forthcoming property of this manuscript is its calculating of the goal of norms and lower bounds of matrix operators taken from the weighted sequence space l(p)(w) onto a novel one defined in the present article as the generalized Fibonacci weighted difference sequence space. In this process, first of all the Fibonacci difference matrix (F) over tilde (r,s) and the space composed of sequences of which (F) over tilde (r,s)-transforms lie in l(p)((w) over tilde), where r,s is an element of R are defined. Additionaly, since the seminormed space l(p)((w) over tilde,(F) over tilde (r,s)) has the absolute homogeneous property, the topological characteristics on it are distributed symmetrically everywhere in the space.Öğe SOME GENERALIZED FIBONACCI DIFFERENCE SPACES DEFINED BY A SEQUENCE OF MODULUS FUNCTIONS(Univ Nis, 2017) Kilinc, Gulsen; Candan, MuratThis paper submits the sequence space l ((F) over cap (r, s) , F, p, u) and l(infinity) ((F) over cap (r, s) , F, p, u) of non-absolute type under the domain of the matrix (F) over cap (r, s) constituted by using Fibonacci sequence and non-zero real number r, s and a sequence of modulus functions. We study some inclusion relations, topological and geometric properties of these spaceses. Further, we give the alpha- beta- and gamma-duals of said sequence spaces and characterization of the classes (l ((F) over cap (r, s) , F, p, u) , X) and (l(infinity) ((F) over cap (r, s) , F, p, u) , X).Öğe SOME NEW SEQUENCE SPACE SDEFINED BY A MODULUS FUNCTION AND AN INFINITE MATRIX IN A SEMINORMED SPACE(Univ Prishtines, 2012) Candan, MuratLet (c) over cap denotes the space of almost convergent sequences introduced by G. G. Lorentz [A contribution to the theory of divergent sequences, Acta Math. 8 0 ( 1948), 167{190]. The main purpose of the present paper is to introduce the sequence spaces w 0 ((A) over cap .p; f; q; s); w ((A) over cap ,p; f; q; s) and w(infinity) ((A) over cap ,p; f; q; s) defined by a modulus function f. Some topological properties of that spaces are examined. Also we exposed some inclusion relations among the variations of the space.Öğe Sınırlı yakınsaklık alanları(İnönü Üniversitesi, 1999) Candan, MuratBu çalışma iki bölümden meydana gelmiştir. İlk be teoremler verildi. İkinci bölümde sınırlı yakınsaklık alanları incelendi..Öğe Vector-Valued FK-Spaces Defined by a Modulus Function and an Infinite Matrix(Chiang Mai Univ, Fac Science, 2014) Candan, MuratThe present paper is devoted to studying on the sequence space lambda (A, X-k, r, f, s) defined by a modulus function f and an infinite matrix A and constructed its FK-structure under some conditions. Finally, we exposed some inclusion relations among the variations of the space. The vector-valued sequence space lambda (A, X-k, r, f, s) as a paranormed space which is a most general form of the space investigated in [1].
