University of MaraghehSahand Communications in Mathematical Analysis2322-580718120210201Some Properties of Lebesgue Fuzzy Metric Spaces1144666710.22130/scma.2020.120854.743ENSugataAdhyaDepartment of Mathematics, The Bhawanipur Education Society College. 5, Lala Lajpat Rai Sarani, Kolkata 700020, West Bengal, India.0000-0001-7106-5707AtasiDeb RayDepartment of Pure Mathematics, University of Calcutta. 35, Ballygunge Circular Road, Kolkata 700019, West Bengal, India.0000-0002-7380-0928Journal Article20200128In this paper, we establish a sequential characterisation of Lebesgue fuzzy metric and explore the relationship between Lebesgue, weak $G$-complete and compact fuzzy metric spaces. We also discuss the Lebesgue property of several well-known fuzzy metric spaces.https://scma.maragheh.ac.ir/article_46667_f59e7b832de5c1c96be81715fb591613.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580718120210201A Note on Some Results for $C$-controlled $K$-Fusion Frames in Hilbert Spaces15344657510.22130/scma.2020.123056.766ENHabibShakooryDepartment of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran.RezaAhmadiResearch Institute for Fundamental Sciences, University of Tabriz, Tabriz, Iran.NaghiBehzadiResearch Institute for Fundamental Sciences, University of Tabriz, Tabriz,
Iran.SusanNamiFaculty of Physic, University of Tabriz, Tabriz, Iran.Journal Article20200314In this manuscript, we study the relation between K-fusion frame and its local components which leads to the definition of a $C$-controlled $K$-fusion frames, also we extend a theory based on K-fusion frames on Hilbert spaces, which prepares exactly the frameworks not only to model new frames on Hilbert spaces but also for deriving robust operators. In particular, we define the analysis, synthesis and frame operator for $C$-controlled $K$-fusion frames, which even yield a reconstruction formula. Also, we define dual of $C$-controlled $K$-fusion frames and study some basic properties and perturbation of them.https://scma.maragheh.ac.ir/article_46575_1c975979396a5c2cf12c24741735cc21.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580718120210201On Approximation of Some Mixed Functional Equations35464666510.22130/scma.2020.127585.801ENAbbasNajatiDepartment of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.BatoolNooriDepartment of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.Mohammad BagherMoghimiDepartment of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran.Journal Article20200628In this paper, we have improved some of the results in [C. Choi and B. Lee, Stability of Mixed Additive-Quadratic and Additive--Drygas Functional Equations. Results Math. 75 no. 1 (2020), Paper No. 38]. Indeed, we investigate the Hyers-Ulam stability problem of the following functional equations<br />\begin{align*}<br /> 2\varphi(x + y) + \varphi(x - y) &= 3\varphi(x)+ 3\varphi(y) \\<br /> 2\psi(x + y) + \psi(x - y) &= 3\psi(x) + 2\psi(y) + \psi(-y).<br />\end{align*}<br />We also consider the Pexider type functional equation \[2\psi(x + y) + \psi(x - y) = f(x) + g(y),\] and the additive functional equation<br />\[2\psi(x + y) + \psi(x - y) = 3\psi(x) + \psi(y).\]https://scma.maragheh.ac.ir/article_46665_3ce38b61e7b850642214401464923acf.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580718120210201Gabor Dual Frames with Characteristic Function Window47574666610.22130/scma.2020.121704.751ENMohammad AliHasankhani FardDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, P.O.Box 546, Rafsanjan, Iran.Journal Article20200326The duals of Gabor frames have an essential role in reconstruction of signals. In this paper we find a necessary and sufficient condition for two Gabor systems $\left(\chi_{\left[c_1,d_1\right)},a,b\right)$ and $\left(\chi_{\left[c_2,d_2\right)},a,b\right)$ to form dual frames for $L_2\left(\mathbb{R}\right)$, where $a$ and $b$ are positive numbers and $c_1,c_2,d_1$ and $d_2$ are real numbers such that $c_1<d_1$ and $c_2<d_2$.https://scma.maragheh.ac.ir/article_46666_d613662078ce4df44a79d834be6b2f64.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580718120210201$K$-orthonormal and $K$-Riesz Bases59724711410.22130/scma.2020.130958.827ENAhmadAhmdiDepartment of Mathematics, Faculty of Science, University of Hormozgan, P.O.Box 7916193145, Bandar Abbas, Iran.0000-0001-9870-2374AsgharRahimiDepartment of Mathematics, Faculty of Science, University of Maragheh, P.O.Box 55136-553, Maragheh, Iran.0000-0003-2095-6811Journal Article20200714Let $K$ be a bounded operator. $K$-frames are ordinary frames for the range $K$. These frames are a generalization of ordinary frames and are certainly different from these frames. This research introduces a new concept of bases for the range $K$. Here we define the $K$-orthonormal basis and the $K$-Riesz basis, and then we describe their properties. As might be expected, the $K$-bases differ from the ordinary ones mentioned in this article.https://scma.maragheh.ac.ir/article_47114_8902cf1717995f11537b68de849abfb0.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580718120210201On New Extensions of Hermite-Hadamard Inequalities for Generalized Fractional Integrals738823941510.22130/scma.2020.121963.759ENHuseyinBudakDepartment of Mathematics, Faculty of Science and Arts, Duzce
University, Duzce, Turkey0000-0001-8843-955XEbruPehlivanDepartment of Mathematics, Faculty of Science and Arts, Duzce
University, Duzce, TurkeyPınarKosemDepartment of Mathematics, Faculty of Science and Arts, Duzce
University, Duzce, TurkeyJournal Article20200220In this paper, we establish some Trapezoid and Midpoint type inequalities for generalized fractional integrals by utilizing the functions whose second derivatives are bounded . We also give some new inequalities for $k$-Riemann-Liouville fractional integrals as special cases of our main results. We also obtain some Hermite-Hadamard type inequalities by using the condition $f^{\prime }(a+b-x)\geq f^{\prime }(x)$ for all $x\in \left[ a,\frac{a+b}{2}\right] $ instead of convexity.https://scma.maragheh.ac.ir/article_239415_3352d66ff13ca0aaf786ddd8dec3bac3.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580718120210201Some bi-Hamiltonian Systems and their Separation of Variables on 4-dimensional Real Lie Groups8910523941910.22130/scma.2020.122380.764ENGhorbanali -HaghighatdoostDepartment of Mathematics,Azarbaijan Shahid Madani University, 53714-161, Tabriz, Iran.SalahaddinAbdolhadi-ZangakaniDepartment of Mathematics, University of Bonab, Tabriz, Iran.RasoulMahjoubi-BahmanDepartment of Mathematics, University of Bonab, Tabriz, Iran.Journal Article20200229In this work, we discuss bi-Hamiltonian structures on a family of integrable systems on 4-dimensional real Lie groups. By constructing the corresponding control matrix for this family of bi-Hamiltonian structures, we obtain an explicit process for finding the variables of separation and the separated relations in detail.https://scma.maragheh.ac.ir/article_239419_91691df474e29d99e062adb4b80f44ae.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580718120210201A Fixed Point Theorem for Weakly Contractive Mappings10712224024410.22130/scma.2020.124853.778ENMortezaSaheliDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.Seyed Ali MohammadMohsenialhosseiniDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.Journal Article20200417In this paper, we generalize the concepts of weakly Kannan, weakly Chatterjea and weakly Zamfirescu for fuzzy metric spaces. Also, we investigate Banach's fixed point theorem for the mentioned classes of functions in these spaces. Moreover, we show that the class of weakly Kannan and weakly Chatterjea maps are subclasses of the class of weakly Zamfirescu maps.https://scma.maragheh.ac.ir/article_240244_312e08cfb7d0abd2e919ed27c0d60e88.pdfUniversity of MaraghehSahand Communications in Mathematical Analysis2322-580718120210201On Some Coupled Fixed Point Theorems with Rational Expressions in Partially Ordered Metric Spaces12313624024510.22130/scma.2020.120323.739ENN.Seshagiri RaoDepartment of Applied Mathematics, School of Applied Natural Sciences, Adama Science and Technology University, Post Box No.1888, Adama, Ethiopia.0000-0003-2409-6513K.KalyaniDepartment of Mathematics, Vignan's Foundation for Science, Technology & Research, Vadlamudi-522213, Andhra Pradesh, India.0000-0003-2409-6513Journal Article20200118The aim of this paper is to prove some coupled fixed point theorems of a self mapping satisfying a certain rational type contraction along with strict mixed monotone property in an ordered metric space. Further, a result is presented for the uniqueness of a coupled fixed point under an order relation in a space. These results generalize and extend known existing results in the literature.https://scma.maragheh.ac.ir/article_240245_ff50f03d2067d187f5a7ed94298209a7.pdf