Journal of Mathematical Extension
Volume:13 Issue: 1, Winter 2019

In this work, some Hardy-Hilbert’s integral inequalities with the best possible constants are proved. Also, some finite and infinite decompositions of some type Hardy-Hilbert’s integral operators are given. Indeed, for a non-negative kernel K, two Kernels K1 and K2 are given such that TK = TK1 + TK2 and TK = TK1  + TK2  and also, Tk1 = cTk2 for every constant c. So, the space of bounded linear operators is not strictly convex. Also, as an application of infinite decomposition of some Hardy-Hilbert’s integral operators, the convergence of some series of hypergeometric functions are given.

In this paper, we have presented and studied the MittagLeffler-Hyers-Ulam stability of a fractional differential equation of second order. We have proved that the differential equation y+αy +βy = 0 is Mittag-Leffler-Hyers-Ulam stable. Then we consider the stability of Lane-Emden equation of second order.

This paper introduces a new generalized denition of cross-entropy for nding the solution of a multi-criteria decision-making (MC-DM) problem. A new interpretation of a belief function in DempsterShafer theory, namely belief function theory, under uncertainty is presented, which is affected in the decision-making process. Belief functions are determined as three elements (i.e., belief degree, uncertainty degree and disbelief degree). Then, a belief measure between an alternative and ideal alternative is calculated by cross entropy to rank alternatives and select the most desirable one. Finally, the efficiency of the proposed CDM method is demonstrated by solving a numerical example.

The purpose of the paper is to present a new generalization of the dual Fibonacci quaternions called the generalized dual bi-periodic Fibonacci quaternions. This new generalization allow us to state several number of dual quaternion sequences in a unique sequence. Furthermore, we give the generating function, the Binet formula, the norm value and some basic properties of these dual quaternions.

‎The matricial ranges of $2\times 2$ complex matrices are revisited‎. ‎Moreover‎, ‎using the standard block-matrix techniques‎, ‎we‎ ‎describe matricial ranges of some special non-quadratic higher order matrices‎. ‎Finally‎, ‎we obtain the matricial ranges of some specific $3\times 3$ matrices‎. ‎Various examples are given as‎ ‎well‎.

We make some ecient modications on the modied secant equation proposed by Zhangand Xu (2001). Then we introduce modied BFGS method using propose secant equation,and obtain some attractive results in theory and practice. We establish the global con-vergence property of the proposed method without convexity assumption on the objectivefunction. Numerical results on some testing problems from CUTEr collection show the pri-ority of the proposed method to some existing modied secant methods in practice

In this study, we introduce a new model called the Extended Exponentiated PowerLindley distribution which extends the Lindley distribution and has increasing, bathtub andupside down shapes for the hazard rate function. It also includes the power Lindley distributionas a special case. Several statistical properties of the distribution are explored, such as thedensity, hazard rate, survival, quantile functions, and moments. Estimation using the maximumlikelihood method and inference on a random sample from this distribution are investigated. Asimulation study is performed to compare the performance of the di®erent parameter estimatesin terms of bias and mean square error. We apply a real data set to illustrate the applicabilityof the new model. Empirical ¯ndings show that proposed model provides better ¯ts than otherwell-known extensions of Lindley distributions.

The article studies the concept of a biprojective and pseudo amenable Banach algebra , where is a continuous homomorphism on and . We show if is contractible, then is biprojective. The converse holds, whenever is either unital or commutative and there exists such that .