Journal of Mathematical Extension
Volume:14 Issue: 2, Spring 2020

The aim of this paper is to given the coincidence and common fixed point of two mappings via R-functin in the setting of ordered partial metric spaces. Result is supported by given an example. An application to the integral equation is also provided.

We investigate the existence of solutions for a multi-singular pointwise defined fractional integro-differential equation under some boundary conditions.

Anchor points are an important subset of the set of extreme efficient points of the Production Possibility Set (PPS) in the Data Envelopment Analysis (DEA). They delineate the efficient from the inefficient part of the PPS frontier. In this paper we present a method to find anchor points of the PPS of the BCC model based on searching weak supporting hyperplane passing through unit under consideration. Then, one theorem is proved creating necessary and sufficient condition for identification of these points. Using numerical examples, we will demonstrate how to use the results.

In this paper, using direct method, we prove the Hyers-Ulam-Rassias stabilityof the some functional equations on Banach lattice.

The intersection graph ΓSI (G) of a group G with identity element e is the graph whose vertex set is the set V (ΓSI (G)) = G − e and two distinct vertices x and y are adjacent in ΓSI (G) if and only if |hxi ∩ hyi| > 1, where hxi is the cyclic subgroup of G generated by x. In this paper, at first we obtain some results for this graph for any Moufang loop. More specially we observe non-isomorphic finite Moufang loops may have isomorphic intersection graphs.

‎ORBIT is a derivative-free trust-region framework that employs a radial basis function (RBF) interpolation to solve the computationally expensive optimization problems‎. ‎The accuracy and stability of RBF interpolation depend on a so-called shape parameter‎, ‎the type of RBF and the number of data points‎. ‎So it is more appropriate to determine these parameters properly‎. ‎In this paper‎, ‎we evaluate the performance of the ORBIT algorithm by different types of RBF‎, ‎different numbers of data points and different shape parameter values‎. ‎We utilize Dolan-More performance profile and More-Wild data profile to investigate the performance of algorithms‎. ‎Finally‎, ‎based on this numerical study we proposed some recommendations for the type of RBF‎, ‎the number of data points and the shape parameter value‎.

Let X be a unitial Banach algebra, G be the set of functions f : [0, 1] → X that are non strongly McShane integrable and L be the set of functions f : [0, 1] → [0, ∞) that are non strongly McShane integrable. The aim of this paper is to show that there is an infinite dimensional closed vector space in G ∪0 and a c-generated algebra in L isomorphic with a free algebra.

In this paper we study the weighted composition operator ψCφ on the Dirichlet type spaces Dp α(D). We show that if the weighted composition operator ψCφ is bounded on such spaces(for 1  p < 2) then the related measure µp,α,ψ is a Carleson measure. Also we show that if the weighted composition operator ψCφ is an isomety on Dp α(D) then ψ.φ is a rotation map on D.

Gamma type functions satisfying the difference functional equations f(x + 1) = g(x)f(x) and limit summability of functions were studied and introduced by R.J. Webster and M.H. Hooshmand, respectively. It is shown that the topic of gamma type functions can be considered as a subtopic of limit summability. Indeed, if ln f is limit summable, then its limit summand function (ln f)σ satisfies (ln f)σ(x) = ln f(x) + (ln f)σ(x − 1) and e(ln f)σ (x) is gamma type function of f(x + 1). In this paper, we introduce and study limit summability of order two, 2-limit summand function fσ2 and its results as gamma type functions of order two and also limit summand of multipliers. Finally, as an application of the study, we obtain a criteria for existence of gamma type function of the function f(x) x and give some related examples and corollaries.

In this paper, we introduce the concept of 2-absorbing semiprimary submodules in modules over a commutative ring with nonzero identity which is a generalization of 2-absorbing primary submodule. Let N be a proper submodule of an R-module M. Then N is said to be a 2-absorbing semiprimary submodule of M if whenever a1a2 ∈ R, m ∈ M and a1a2m ∈ N, then a1a2 ∈ (N :R M) or a1m ∈ N or an 2 m ∈ N, for some positive integer n. We have given an example and proved number of results concerning 2-absorbing semiprimary submodules.

In this paper, there has been developed an adaptive method with memory based on the on the first two steps of the general optimal method without memory by Kung and Traub. Included is convergence analysis along with numerical implementations. The proposed adaptive method with memory can increase the efficiency index of the optimal method without memory as high as possible while reusing all the available information of the functional evaluations in the previous iteration for this purpose. Also, we discuss the numerical stability from the point of basins of attraction.

There are several methods to compute the optimal bounds of the objective function for interval quadratic programming (IQP) problems, but no method has yet been suggested to calculate a set of optimal solutions of IQP problems. This paper presents an accurate set of optimal solutions for the interval quadratic programming problems. The optimal solution of the quadratic programming problem is not essentially an extreme point. We rst propose conditions that make the optimal solutions of the IQP to extreme points and then, using these conditions, we compute the exact set of optimal solutions for the IQP problem.