Transactions of A Razmadze Mathematical Institute最新文献

In this work, we give sufficient conditions for the existence of a mild solution for some impulsive integro-differential equations in Banach spaces. We study the existence without assuming the Lipschitz condition on the nonlinear term $f$. The compactness on the $C_0\text{-}semigroup{\left(T\left(t\right)\right)}_{t\ge 0}$ in a Banach space is not needed. We use Hausdorff’s measure of noncompactness, resolvent operators and Darbo’s fixed point Theorem to obtain the main result of this work.

In this work,we consider iterative methods for solving a class of equilibrium problems in Hadamard Manifolds by using the auxiliary principle techniques. We also discuss the convergence of sequences generated by the algorithms.

We first establish some Ostrowski type inequalities for mappings whose second derivatives absolute values are convex. Then we give some special cases of these inequalities which provide extensions of those given in earlier works. Finally, some applications of these inequalities for special means are also provided.

Positive homogeneous functions on $R$ of a negative degree are characterized by a new counterpart of the Euler’s homogeneous function theorem using quantum calculus and replacing the classical derivative operator by Jackson derivative. As application we start by characterizing the harmonic functions associated to Jackson derivative. Then, the solution of the Cauchy problem associated to the analogue of the Euler operator is given. Using this solution we study the associated $\nu$-potential. Its Markovianity property is treated.

In this paper, our main objective is to establish certain new fractional integral by applying the Saigo hypergeometric fractional integral operators and by employing some integral transforms on the resulting formulas, we presented their image formulas involving the product of the generalized $k$-Mittag-Leffler function. Furthermore, We develop a new and further generalized form of the fractional kinetic equation involving the product of the generalized $k$-Mittag-Leffler function. The manifold generality of the generalized $k$-Mittag-Leffler function is discussed in terms of the solution of the fractional kinetic equation and their graphical interpretation is interpreted in the present paper. The results obtained here are quite general in nature and capable of yielding a very large number of known and (presumably) new results.

Let $\Omega \in L^2\left(S^{n-1}\right)$ be a homogeneous function of degree zero and $b$ be a BMO or Lipschitz function. In this paper, we obtain some boundedness of the parametrized Littlewood–Paley operators and their high-order commutators on Herz spaces with variable exponent.

In this paper, we establish a companion of Ostrowski type inequalities for mappings of bounded variation and the quadrature formula is also provided.

In this paper, we introduce and study some non-absolute type spaces $l_{\infty }(u,\lambda ,{\Delta }_v^m)$, $c_0(u,\lambda ,{\Delta }_v^m)$ and $c(u,\lambda ,{\Delta }_v^m)$, which are $\mathrm{BK}$-spaces. Moreover, we prove that these spaces are linearly isomorphic to the spaces $l_{\infty },c_0$ and $c$. We also make an effort to establish some inclusion relations between these spaces. Furthermore, we find the Schauder basis for these spaces and also determine the $\alpha$-, $\beta$- and $\gamma$-duals of these spaces.

The aim of this paper is to prove fixed point results under $(\psi ,\varphi )$-weak contractive condition for continuous weak compatible mappings in ordered $b$-metric spaces. The results proved herein generalize, modify and unify some recent results of the existing literature. An application demonstrating the usability of our established results is also discussed besides furnishing an illustrative example.

The magneto hydrodynamic boundary layer flow with heat and mass transfer of Williamson nanofluid over a stretching sheet with variable thickness and variable thermal conductivity under the radiation effect is examined. It is assumed that the sheet is non-flat. The governing partial differential equations are reduced to nonlinear coupled ordinary differential equations by applying the suitable similarity transformations. These nonlinear coupled ordinary differential equations, subject to the appropriate boundary conditions, are then solved by using spectral quasi-linearisation method (SQLM). The effects of the physical parameters on the flow, heat transfer and nanoparticle concentration characteristics of the problem are presented through graphs and are discussed in detailed. Numerical values of skin friction co-efficient and Nusselt number with different parameters were computed and analysed.