rss_2.0General Mathematics FeedSciendo RSS Feed for General Mathematics Mathematics 's Cover and quotients of positive linear operators<abstract><title style='display:none'>Abstract</title><p>We consider the classical <italic>Szász-Mirakyan</italic> and <italic>Szász-Mirakyan-Durrmeyer</italic> operators, as well as a <italic>Kantorovich</italic> modification and a discrete version of it. The images of exponential functions under these operators are determined. We establish estimates involving differences and quotients of these images.</p></abstract>ARTICLE2020-12-31T00:00:00.000+00:00Upper bound of second Hankel determinant for bi-univalent functions with respect to symmetric conjugate<abstract><title style='display:none'>Abstract</title><p>In this article, our aim is to estimate an upper bounds for the second Hankel determinant <italic>H</italic><sub>2</sub>(2) of a certain class of analytic and bi-univalent functions with respect to symmetric conjugate defined in the open unit disk <italic>U</italic>.</p></abstract>ARTICLE2020-12-31T00:00:00.000+00:00On the reconstruction via Urysohn-Chlodovsky operators<abstract><title style='display:none'>Abstract</title><p>The main first goal of this work is to introduce an Urysohn type Chlodovsky operators defined on positive real axis by using the Urysohn type interpolation of the given function <italic>f</italic> and bounded on every finite subinterval. The basis used in this construction are the Fréchet and Prenter Density Theorems together with Urysohn type operator values instead of the rational sampling values of the function. Afterwards, we will state some convergence results, which are generalization and extension of the theory of classical interpolation of functions to operators.</p></abstract>ARTICLE2020-12-31T00:00:00.000+00:00Differential subordination results for holomorphic functions associated with Wanas Operator and Poisson Distribution series<abstract><title style='display:none'>Abstract</title><p>In the current paper, we introduce a new family for holomorphic functions defined by Wanas operator associated with Poisson distribution series. Also we derive some interesting geometric properties for functions belongs to this family.</p></abstract>ARTICLE2020-12-31T00:00:00.000+00:00Some univalence conditions related to a general integral operator<abstract><title style='display:none'>Abstract</title><p>For some classes of analytic functions <italic>f</italic>, <italic>g</italic>, <italic>h</italic> and <italic>k</italic> in the open unit disk 𝕌, we consider the general integral operator 𝒢<italic><sub>n</sub></italic>, that was introduced in a recent work [1] and we obtain new conditions of univalence for this integral operator. The key tools in the proofs of our results are the Pascu’s and the Pescar’s univalence criteria, as well as the Mocanu’s and Şerb’s Lemma. Some corollaries of the main results are also considered. Relevant connections of the results presented here with various other known results are briefly indicated.</p></abstract>ARTICLE2020-12-31T00:00:00.000+00:00A note on Jordan’s inequality<abstract><title style='display:none'>Abstract</title><p>In this paper we obtain some bounds in terms of polynomials for the function <inline-formula><alternatives><inline-graphic xmlns:xlink="" xlink:href="graphic/j_gm-2020-0019_eq_001.png"/><mml:math xmlns:mml="" display="inline"><mml:mrow><mml:mfrac><mml:mrow><mml:mo>sin</mml:mo><mml:mi>x</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:mfrac></mml:mrow></mml:math><tex-math>{{\sin x} \over x}</tex-math></alternatives></inline-formula>, <italic>x</italic> ∈ [0, π].</p></abstract>ARTICLE2020-12-31T00:00:00.000+00:00Some Bullen-type inequalities for conformable fractional integrals<abstract><title style='display:none'>Abstract</title><p>In this study, the author has established a new lemma and Bullen-type inequalities for conformable fractional integrals. Also, it is given some applications involving Bullen type integral inequalities for differentiable functions to show the results.</p></abstract>ARTICLE2020-12-31T00:00:00.000+00:00Ulam stability for Thunsdorff and Cauchy-Schwarz equations<abstract><title style='display:none'>Abstract</title><p>We consider the equality case in Thunsdorff inequality and Cauchy-Schwarz inequality. For these two equations we prove Ulam stability.</p></abstract>ARTICLE2020-12-31T00:00:00.000+00:00Geometric properties of some applications of the Tremblay operator<abstract><title style='display:none'>Abstract</title><p>By this research notes, the well-known Tremblay operator and certain core knowledge therewith are firstly introduced and an extensive result containing numerous (analytic and) geometric properties (of possible applications of the related operator) along with a number of special implications are then constituted. As method for proving, the well-known assertion proposed by [8] is also considered there.</p></abstract>ARTICLE2020-12-31T00:00:00.000+00:00Book Review: Approximation with Positive Linear Operators and Linear Combinations By: Vijay Gupta, Gancho Tachev Series: Developments in Mathematics, Volume 50, Springer, Cham, 2017 study of fractional integro-differential equations via Hilfer-Hadamard fractional derivative<abstract><title style='display:none'>Abstract</title><p>In this paper, we investigate the existence of solution of integro-differential equations (IDEs) with Hilfer-Hadamard fractional derivative. The main results are obtained by using Schaefer’s fixed point theorem. Some Ulam stability results are presented.</p></abstract>ARTICLE2019-12-21T00:00:00.000+00:00Some strong and weak form of z-continuity via<abstract><title style='display:none'>Abstract</title><p>This paper mainly dedicated on overview of zero sets in Ideal topological spaces. We also introduce a new class of functions which generalizes the class of continuous functions and investigate its position in the hierarchy of continuous functions on Ideal topological spaces. Moreover, these new sets (zero*-ℐ-set) which is a pragmatic approach to characterize completely <italic>Hausdorff</italic> spaces.</p></abstract>ARTICLE2019-12-21T00:00:00.000+00:00Properties of the intermediate point from a mean value theorem of the integral calculus - II<abstract><title style='display:none'>Abstract</title><p>In this paper we consider two continuous functions <italic>f, g</italic> : [<italic>a, b</italic>] → ℝ and we study for these ones, under which circumstances the intermediate point function is four order di erentiable at the point <italic>x</italic> = <italic>a</italic> and we calculate its derivative.</p></abstract>ARTICLE2019-12-21T00:00:00.000+00:00Forgotten topological index and reduced Zagreb index of four new operations of graphs<abstract><title style='display:none'>Abstract</title><p>Indulal and Balakrishnan (2016) have put forward the Indu-Bala product and based on this product four new operations are defined by the authors of this manuscript in the paper “Four new operations of graphs based on Indu-Bala product and the Zagreb indices”. In this paper we establish explicit formulas of the forgotten topological index and reduced second Zagreb index in connection with these new operations of graphs.</p></abstract>ARTICLE2019-12-21T00:00:00.000+00:00Arens simultaneously factorization<abstract><title style='display:none'>Abstract</title><p>Let <italic>X</italic> be a Banach bimodule over a Banach algebra 𝒜. We shall seek conditions under which (1) <italic>X</italic> and its dual factorize on the same side or (2) <italic>X</italic> factors on the left (or right) if and only if its second conjugate space has a left (or right) unit.</p></abstract>ARTICLE2019-12-21T00:00:00.000+00:00Book Review: Recent Advances in Constructive Approximation Theory By: V. Gupta, T.M. Rassias, P.N. Agrawal, A.M. Acu Springer Optim. Appl. 138, Springer, Cham, 2018, DOI 10.1007/978-3-319-92165-5 of classical and fractional inequalities having congruity on time scale calculus<abstract><title style='display:none'>Abstract</title><p>In this paper, we find accordance of some classical inequalities and fractional dynamic inequalities. We find inequalities such as Radon’s inequality, Bergström’s inequality, Rogers-Hölder’s inequality, Cauchy-Schwarz’s inequality, the weighted power mean inequality and Schlömilch’s inequality in generalized and extended form by using the Riemann-Liouville fractional integrals on time scales.</p></abstract>ARTICLE2019-12-21T00:00:00.000+00:00On Neighbor chromatic number of grid and torus graphs<abstract><title style='display:none'>Abstract</title><p>A set <italic>S</italic> ⊆ <italic>V</italic> is a neighborhood set of a graph <italic>G</italic> = (<italic>V, E</italic>), if <italic>G</italic> = ∪<italic><sub>v∈S</sub></italic> 〈 <italic>N</italic>[<italic>v</italic>] 〉, where 〈 <italic>N</italic>[<italic>v</italic>] 〉 is the subgraph of a graph <italic>G</italic> induced by <italic>v</italic> and all vertices adjacent to <italic>v</italic>. A neighborhood set <italic>S</italic> is said to be a neighbor coloring set if it contains at least one vertex from each color class of a graph <italic>G</italic>, where color class of a colored graph is the set of vertices having one particular color. The neighbor chromatic number χ<italic><sub>n</sub></italic> (<italic>G</italic>) is the minimum cardinality of a neighbor coloring set of a graph <italic>G</italic>. In this article, some results on neighbor chromatic number of Cartesian products of two paths (grid graph) and cycles (torus graphs) are explored.</p></abstract>ARTICLE2019-12-21T00:00:00.000+00:00Notes on certain p-valent functions<abstract><title style='display:none'>Abstract</title><p>Let <italic>A<sub>p</sub></italic> be the class of functions <italic>f</italic>(<italic>z</italic>) which are analytic in the open unit disk <italic>U</italic>. Applying some subordinations for functions, some interesting properties for <italic>f</italic>(<italic>z</italic>) ∈<italic>A<sub>p</sub></italic> are showed. Our results are generalizations for results given before.</p></abstract>ARTICLE2019-12-21T00:00:00.000+00:00On graded derivations of superalgebras<p>In this paper, we find conditions under which the bracket defined by a graded derivation on a Lie superalgebra (<italic>g</italic>, [, ]) is skew-supersymmetry and satisfies the super Jacobi identity, so it defines the structure of a Lie superalgebra on <italic>g.</italic></p>ARTICLE2020-07-31T00:00:00.000+00:00en-us-1