Volume 12 (2020), Number 2
New Differential Operator Involving the -Ruscheweyh Derivative and the Symmetric Differential
Author(s): KHALID ALSHAMMARI and MASLINA DARUS
Abstract: In this paper, we define a new differential operator involving -calculus by using a familiar technique which is a Hadamard product. We use convolution between -analogue of the Ruscheweyh derivative by Aldweby and Darus [1] and the symmetric Salagean differential operator by Ibrahim and Darus [2]. We study some properties of the new operator such as the negative coefficients estimate, growth and the radii of starlikeness and convexity.
DownloadA Landau’s Inequality for Semigroups Revisited
Author(s): GEORGE A. ANASTASSIOU
Abstract: H. Kraljevič and S. Kurepa in 1970 ([13]) proved a nice Landau type inequality for semigroups by making use of Taylor’s formula with integral remainder for semigroups, which has been a traditional method for proving such inequalities. The author offers another method in the semigroups and reproves the above result by using his earlier result about Ostrowski inequalities for semigroups, see [1], Chapter 16, pp. 259-289. He finds his method easier and convenient. An application is given at the end.
DownloadPositive Solutions to Caputo-Hadamard Fractional Integro-Differential Equations With Integral Boundary Conditions
Author(s): ABDELOUAHEB ARDJOUNI
Abstract: In this article, we study the existence and uniqueness of positive solutions of a Caputo-Hadamard fractional integro-differential equation with integral boundary conditions. The fixed point theorems and the method of upper and lower solutions are used to obtain the desired results. An example illustrating the main results is presented.
DownloadAn Integral Equation From Physics - a Synthesis Survey - Part III
Author(s): MARIA DOBRIȚOIU
Abstract: This is the third part of the synthesis survey on the study of the integral equation from physics: and contains the results concerning the approximation of its solution by applying numerical methods. This part ends with an example.
DownloadSome Integral Inequalities for Operator Monotone Functions
Author(s): SILVESTRU SEVER DRAGOMIR
Abstract: In this paper we prove among others that for an operator monotone function on , where is a bounded continuous field of positive operators in defined on a locally compact Hausdorff space with a bounded Radon measure that satisfy certain conditions while are nonnegative with . Some particular inequalities of interest are also provided.
DownloadCharacterizations of Strongly Generalized Convex Functions
Author(s): MUHAMMAD ASLAM NOOR and KHALIDA INAYAT NOOR
Abstract: In this paper, we define and consider some new concepts of the strongly general convex functions with respect to two arbitrary functions. Some properties of the strongly generalized convex functions are investigated under suitable conditions. It is shown that the optimality conditions of the strongly generalized convex functions are characterized by a class of variational inequalities, which is called the strongly generalized variational inequality. Some special cases also discussed. Results obtained in this paper can be viewed as refinement and improvement of previously known results.
DownloadOn the Generalized Ostrowski Type Inequalities via Tempered Fractional Integrals
Author(s): MEHMET ZEKI SARIKAYA and MEHMET EYÜP Kİ̇Rİ̇Ş
Abstract: In this paper, we have found a new version of the Ostrowski type inequality for tempered Riemann-Liouville fractional integrals. In addition, some relevant results have been obtained.
DownloadMath Problems - Solutions, Observations and Comments
Author(s): MARIA DOBRIȚOIU
Abstract: The paper aims to present some theoretical methodological considerations regarding the solving of math problems. Thus, there are presented theoretical aspects regarding the formation of mathematical thought, the activity of education and training through mathematics, types of learning in mathematics and forms of organizing the activities in mathematical education in Romania, reason for which the References that were used are entirely in Romanian. The paper also contains some math problems solved: geometry, algebra or even arithmetic problems, and the solutions are accompanied by observations and possible methodical comments.
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