• East Asian mathematical journal
• /
• v.32 no.3
• /
• pp.319-332
• /
• 2016

In this paper, we introduce the notion of generalized ${\alpha}-{\psi}$-Geraghty multivalued mappings and investigate the existence of a xed point of such multivalued mappings. We present a concrete example and an application on integral equations illustrating the obtained results.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.2
• /
• pp.421-438
• /
• 2015

In this paper, we study the existence of classical and generalized solutions for nonlinear differential inclusions $x^{\prime}(t){\in}F(t,x(t))$ in Hilbert spaces in which the multifunction F on the right-hand side is hemicontinuous and satisfies the semimonotone condition or is condensing. Our existence results are obtained via the selection and fixed point methods by reducing the problem to an ordinary differential equation. We first prove the existence theorem in finite dimensional spaces and then we generalize the results to the infinite dimensional separable Hilbert spaces. Then we apply the results to prove the existence of the mild solution for semilinear evolution inclusions. At last, we give an example to illustrate the results obtained in the paper.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.6
• /
• pp.1773-1781
• /
• 2018

The Radon transform introduced by J. Radon in 1917 is the integral transform which is widely applicable to tomography. Here we study the discrete version of the Radon transform. More precisely, when $C({\mathbb{Z}}^n_p)$ is the set of complex-valued functions on ${\mathbb{Z}}^n_p$. We completely determine the subset of $C({\mathbb{Z}}^n_p)$ whose elements can be recovered from its Radon transform on ${\mathbb{Z}}^n_p$.