Journal of Mathematical Analysis and Convex Optimization
Volume:2 Issue: 1, 2021

In this paper we obtain some new multiplicative inequalities for Heinz operator mean.

‎A numerical approach based on Bernstein polynomials is presented to unravel optimal control of nonlinear systems. The operational matrices of differentiation, integration and product are introduced. Then, these matrices are implemented to decrease the solution of nonlinear optimal control problem to the solution of the quadratic programming problem which can be solved with many algorithms and softwares. This method is easy to implement it with an accurate solution. Some examples are included to demonstrate the validity and applicability of the technique.

Let $widetilde{{C}_{varphi}}$ be the Aluthge transform of composition operator on $L^{2}(Sigma)$. The main result of this paper is characterizations of Aluthge transform of composition operators in some operator classes that are weaker than hyponormal, such as hyponormal, quasihyponormal, paranormal, $*$-paranormal on $L^{2}(Sigma)$. Moreover, to explain the results, we provide several useful related examples to show that $widetilde{{C}_{varphi}}$ lie between these classes.

The definition of bipolar multiplicative metric space is introduced in this article, and in this space some properties are derived. Multiplicative contractions for covariant and contravariant maps are defined and fixed points are obtained. Also, some fixed point results of covariant and contravariant maps satisfying multiplicative contraction conditions are proved for bipolar multiplicative metric spaces. Moreover, Banach contraction principle and Kannan fixed point theorem are generalized.

The objective of this work is to investigate the infl uence of boundary conditions at depth soil on the development of methods to determine the soil′s apparent thermal diffusivity based on solution of inverse problems of a heat-transfer equation. Experimental investigations were carried out to establish the influence of boundary conditions at depth in soil on the solution of inverse problems of modeling of heat transfer in soils. For this purpose, 1 soil profile in the land at different depths (x=0, 5, 10, 15,  20, 40, 60 cm) thermal sensors (Temperature recorder Elitech RC-4) have been installed to measure soil temperatures depending on time and depths. Based on these data, the apparent  thermal diffusivity in soils was calculated using the classical (layered) and proposed (point) methods developed for the case with one and two harmonics, and they were compared and the calculated characteristics were compared with the experimental results. It was found that the proposed point methods best reflect the movement of heat in the soil profile.

In this paper we prove the Riesz-Thorian interpolation theo-rem for weighted Orlicz and weighted Morrey Spaces.

The aim of this note is to show that the main conclusion of a recent paper by Sadiq Basha [S. Sadiq Basha, Global optimization in metric spaces with partial orders, emph{Optimization, 63 (2014), 817-825}] can be obtained as a consequence of corresponding existing results in fixed point theory in the setting of partially ordered metric spaces. Moreover, by a similar approach, we prove that in the paper [V. Pragadeeswarar, M. Marudai, Best proximity points: approximation and optimization in partially ordered metric spaces, emph{Optim. Lett. 7 (2013), 1883–1892}] the results are not real generalizations but particular cases of existing fixed point theorems in the literature.

S. G. Mikhlin proved the boundedness of the Fourier multiplier operator in the classical Lebesgue space if the multiplier function is a bounded function. In cite{MWW}, the authors obtained the same result of the classical Morrey space. In this paper, we prove that Mikhlin operator with bounded multiplier function is bounded operator on Morrey space with variable exponent which is containing the classical Lebesgue space with variable exponent and the classical Morrey space.

In this paper, we review some properties of the entropy of random dynamical systems. We define a local entropy map for random dynamical systems and study some of its properties. We extract the entropy of random dynamical systems from the introduced map.

‎In this paper‎, ‎we study character amenability of semigroup algebras `ell^{1}(S)` and weighted semigroup algebras $ ell^{1} (S,omega)$‎, ‎for a certain semigroups such as right(left) zero semigroup‎, ‎rectangular band semigroup‎, ‎band semigroup and uniformly locally finite inverse semigroup‎. ‎In particular‎, ‎we show that for a right (left) zero semigroup or a rectangular band semigroup‎, ‎character amenability‎, ‎amenability‎, ‎pseudo‎ - ‎amenability of $ ell^{1} (S,omega)$‎, ‎for each weight $ omega $‎, ‎are equivalent‎. ‎We also show that for an archimedean semigroup $ S $‎, ‎character pseudo‎ - ‎amenability‎, ‎amenability‎, ‎approximate amenability and pseudo-amenable of $ ell^{1}(S) $ are equivalent‎.

‎The present research paper is concerned about a couple of optimal inequalities for the Casorati curvature of submanifolds in an $({varepsilon})$-almost para-contact manifolds precisely $(varepsilon)$-Kenmotsu manifolds endowed with semi-symmetric metric connection (briefly says $SSM$) by adopting the T‎. ‎Opreachr(chr('39')39chr('39'))s optimization technique.‎

In this paper‎, ‎the polynomial differential quadrature method (PDQM) is implemented to find the numerical solution of the generalized Black-Scholes partial differential equation‎. ‎The PDQM reduces the problem into a system of first order non-linear differential equations and then‎, ‎the obtained system is solved by optimal four-stage‎, ‎order three strong stability-preserving time-stepping Runge-Kutta (SSP-RK43) scheme‎. ‎Numerical examples are given to illustrate the efficiency of the proposed method‎.