University of MaraghehSahand Communications in Mathematical Analysis2322-580719220220601On New Integral Inequalities via Geometric-Arithmetic Convex Functions with Applications11425096210.22130/scma.2021.535821.971ENMerveAvcı ArdıçAdıyaman University, Faculty of Science and Arts, Department of Mathematics, Adıyaman, Turkey.0000-0002-8630-0148Ahmet OcakAkdemirAğrı İbrahim Çeçen University, Faculty of Science and Letters, Department of Mathematics, 04100, Ağrı, Turkey.ErhanSetOrdu University, Faculty of Science and Letters, Department of Mathematics,Ordu, Turkey.Journal Article20210811In this study, new Hermite-Hadamard type inequalities are generated for geometric-arithmetic functions with the help of an integral equation proved for differentiable functions. In proofs, some classical integral inequalities, such as H\"{o}lder's inequality, basic definitions and known mathematical analysis procedures are used. The third part of the study includes various applications confirming the accuracy of the generated results. A brief conclusion of the study has been given in the last part of the paper.https://scma.maragheh.ac.ir/article_250962_e19d8746290553c442a01e7c1d29896f.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580719220220601Fixed Point Results for $F$-Hardy-Rogers Contractions via Mann's Iteration Process in Complete Convex $b$-Metric Spaces153225166510.22130/scma.2022.528127.929ENIsaYildirimDepartment of Mathematics, Faculty of Science, Ataturk University, Erzurum, 25240, Turkey.0000-0001-6165-716XJournal Article20210412In this paper, we give a definition of the $F$-Hardy-Rogers contraction of Nadler type by eliminating the conditions $(F3)$ and $(F4)$. And, we obtain some fixed point theorems for such mappings using Mann's iteration process in complete convex $b$-metric spaces. We also give an example in order to support the main results, which generalize some results in [5,6].https://scma.maragheh.ac.ir/article_251665_598b30839852e9f5f5ebf0024378a1e3.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580719220220601Essential Norm of the Generalized Integration Operator from Zygmund Space into Weighted Dirichlet Type Space334725196610.22130/scma.2022.521137.888ENFaribaAlighadrDepartment of Mathematics, Sarab Branch, Islamic Azad University, Sarab, Iran.HamidVaeziDepartment of Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.Department of Mathematics, Sarab Branch, Islamic Azad University, Sarab, Iran.MostafaHassanlooEngineering Faculty of Khoy, Urmia University of Technology, Urmia, Iran.0000-0002-9213-2574Journal Article20201214Let $H(\mathbb{D})$ be the space of all analytic functions on the open unit disc $\mathbb{D}$ in the complex plane $\mathbb{C}$. In this paper, we investigate the boundedness and compactness of the generalized integration operator<br />$$I_{g,\varphi}^{(n)}(f)(z)=\int_0^z f^{(n)}(\varphi(\xi))g(\xi)\ d\xi,\quad z\in\mathbb{D},$$ from Zygmund space into weighted Dirichlet type space, where $\varphi$ is an analytic self-map of $\mathbb{D}$, $n\in\mathbb{N}$ and $g\in H(\mathbb{D})$. Also we give an estimate for the essential norm of the above operator.https://scma.maragheh.ac.ir/article_251966_ddba7c527ec8fcace5d324b22d964021.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580719220220601The Study of Felbin and $BS$ Fuzzy Normed Linear Spaces496425207910.22130/scma.2022.544742.1033ENFarnazYaqub AzariDepartment of Mathematics, Sahand University of Technology, P.O.Box 53318-17634, Tabriz, Iran.0000-0002-0308-7178IldarSadeqiDepartment of Mathematics, Sahand University of Technology, P.O.Box 53318-17634, Tabriz, Iran.0000-0001-5336-6186Journal Article20211212In this paper, we first show that the induced topologies by Felbin and Bag-Samanta type fuzzy norms on a linear space $X$ are equivalent. So all results in Felbin-fuzzy normed linear spaces are valid in Bag-Samanta fuzzy normed linear spaces and vice versa. Using this, we will be able to define a fuzzy norm on $FB(X,Y)$, the space of all fuzzy bounded linear operators from $X$ into $Y$, where $X$ and $Y$ are fuzzy normed linear spaces.https://scma.maragheh.ac.ir/article_252079_e381e776c648062c670cd7f438f1c4bf.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580719220220601On Some New Extensions of Inequalities of Hermite-Hadamard Type for Generalized Fractional Integrals657925248310.22130/scma.2022.539417.992ENHuseyinBudakDepartment of Mathematics, Faculty of Science and Arts, Duzce
University, Duzce, Turkey.0000-0001-8843-955XCandanCan BilişikDepartment of Mathematics, Faculty of Science and Arts, Duzce
University, Duzce, Turkey.0000-0001-5649-284XMehmet ZekiSarikayaDepartment of Mathematics, Faculty of Science and Arts, Duzce
University, Duzce, Turkey.0000-0002-6165-9242Journal Article20210921In this paper, we establish some inequalities for generalized fractional integrals by utilizing the assumption that the second derivative of $\phi (x)=\varpi \left( \frac{\kappa _{1}\kappa _{2}}{\mathcal{\varkappa }}\right) $ is bounded. We also prove again a Hermite-Hadamard type inequality obtained in [34] under the condition $\phi ^{\prime }\left( \kappa_{1}+\kappa _{2}-\mathcal{\varkappa }\right) \geq \phi ^{\prime }(\mathcal{\varkappa })$ instead of harmonically convexity of $\varpi $. Moreover, some new inequalities for $k$-fractional integrals are given as special cases of main results.https://scma.maragheh.ac.ir/article_252483_5c418ef6a00ed8e07a0b5e2b742f20c3.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580719220220601Corrigenda: ''$\omega b-$Topological Vector Spaces''818925248410.22130/scma.2021.537576.979ENMadhuRamDepartment of Mathematics, University of Jammu, Jammu-180006, India.0000-0001-6583-0978Journal Article20210826In this corrigenda, we have pointed out that Example 2.7, Corollary 3.7 and Corollary 5.3 in the paper: $\omega b-$Topological Vector Spaces, WSEAS Trans. Math. 19 (2020), $119-132$, by Latif are incorrect. We have also presented the corrected version of these results. Furthermore, we introduce and study some new classes of topological vector spaces.https://scma.maragheh.ac.ir/article_252484_0e4b274e4fab6f1e1cad5edc8bf666c3.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580719220220601A New and Faster Iterative Scheme Including Generalized $\alpha$-nonexpansive Mappings in Banach Spaces9111125354410.22130/scma.2022.548031.1057ENAsgharRahimiDepartment of Mathematics, University of Maragheh, Maragheh, Iran.0000-0003-2095-6811AliRezaeiDepartment of Mathematics, University of Maragheh, Maragheh, IranBayazDarabyDepartment of Mathematics, University of Maragheh, Maragheh, Iran.0000-0001-6872-8661MostafaGhasemiDepartment of Mathematics, University of Maragheh, Maragheh, Iran.Journal Article20220202In this paper, we proposed a new iterative process to approximate fixed point of generalized $\alpha$-nonexpansive<br />mappings and show that the coefficient used in the proposed iterative process play a fundamental role in the rate of convergence. We compare the speed of convergence of new iterative process with other well-known iterative process by using numerical examples. Finally, by using new iterative process, we obtained some weak and strong convergence theorems for generalized $\alpha$-nonexpansive mappings in a Banach space.https://scma.maragheh.ac.ir/article_253544_425d0661899a3e86795c69cdcfeab4b3.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580719220220601Approximation by Fuzzy $(p,q)$-Bernstein-Chlodowsky Operators11313225248610.22130/scma.2022.524506.910ENEsma YildizOzkanDepartment of Mathematics, Faculty of Science, Gazi University, P.O.Box 06500, Ankara, Turkey.0000-0003-1283-833XJournal Article20210203In this study, we purpose to extend approximation properties of the $ (p,q)$-Bernstein-Chlodowsky operators from real function spaces to fuzzy function spaces. Firstly, we define fuzzy $ (p,q)$-Bernstein-Chlodowsky operators, and we give some auxiliary results. Later, we give a fuzzy Korovkin-type approximation theorem for these operators. Additionally, we investigate rate of convergence by using first order fuzzy modulus of continuity and Lipschitz-type fuzzy functions. Eventually, we give an estimate for fuzzy asymptotic expansions of the fuzzy $ (p,q)$-Bernstein-Chlodowsky operators.https://scma.maragheh.ac.ir/article_252486_222e93a0f3bc285204199af7020a5ff5.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580719220220601The Generalized Inequalities via Means and Positive Linear Mappings13314825293610.22130/scma.2022.544128.1028ENLeilaNasiriDepartment of Mathematics and computer science, Faculty of science, Lorestan University, Khorramabad, Iran.MehdiShamsDepartment of Statistics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran.0000-0002-9645-9195Journal Article20211202In this paper, we establish further improvements of the Young inequality and its reverse. Then, we assert operator versions corresponding them. Moreover, an application including positive linear mappings is given. For example, if $A,B\in {\mathbb B}({\mathscr H})$ are two invertible positive operators such that $0\begin{align*}<br />& \Phi ^{2} \bigg(A \nabla _{\nu} B+ rMm \left( A^{-1}+A^{-1} \sharp_{\mu} B^{-1} -2 \left(A^{-1} \sharp_{\frac{\mu}{2}} B^{-1} \right)\right)\\<br />& \qquad +\left(\frac{\nu}{\mu} \right) Mm \bigg(A^{-1}\nabla_{\mu} B^{-1} -A^{-1} \sharp_{\mu} B^{-1}<br />\bigg)\bigg) \\<br />& \quad \leq \left( \frac{K(h)}{ K\left( \sqrt{{h^{'}}^{\mu}},2 \right)^{r^{'}}} \right) ^{2} \Phi^{2} (A \sharp_{\nu} B),<br />\end{align*}<br />where $r=\min\{\nu,1-\nu\}$, $K(h)=\frac{(1+h)^{2}}{4h}$, $h=\frac{M}{m}$, $h^{'}=\frac{M^{'}}{m^{'}}$ and $r^{'}=\min\{2r,1-2r\}$. The results of this paper generalize the results of recent years. https://scma.maragheh.ac.ir/article_252936_f6ac497404975f95882a8c19bf1a34df.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580719220220601On Uncountable Frames and Riesz Bases in Nonseparable Banach Spaces14917025248710.22130/scma.2021.523500.905ENMigdadIsmailovBaku State University, Institute of Mathematics and Mechanics of the NAS of Azerbaijan.Journal Article20210121Some generalizations of Besselian, Hilbertian systems and frames in nonseparable Banach spaces with respect to some nonseparable Banach space $K$ of systems of scalars are considered in this work. The concepts of uncountable $K$-Bessel, $K$-Hilbert systems, $K$-frames and $K^{*} $-Riesz bases in nonseparable Banach spaces are introduced. Criteria of uncountable $K$-Besselianness, $K$-Hilbertianness for systems, $K$-frames and unconditional $K^{*} $-Riesz basicity are found, and the relationship between them is studied. Unlike before, these new facts about Besselian and Hilbertian systems in Hilbert and Banach spaces are proved without using a conjugate system and, in some cases, a completeness of a system. Examples of $K$-Besselian systems which are not minimal are given. It is proved that every $K$-Hilbertian systems is minimal. The case where $K$ is an space of systems of coefficients of uncountable unconditional basis of some space is also considered.https://scma.maragheh.ac.ir/article_252487_22bde7068edb87cf8c0a534e9a8ac4aa.pdf