Best proximity point of modified Suzuki-Edelstein-Geraghty type proximal contractions
EASL-Vol. 3 (2020), Issue 4, pp. 94 – 104 Open Access Full-Text PDF
Leta Bekere Kumssa
Abstract: In this paper, we introduce the notion of modified Suzuki-Edelstein-Geraghty proximal contraction and prove the existence and uniqueness of best proximity point for such mappings. Our results extend and unify many existing results in the literature. We draw corollaries and give illustrative example to demonstrate the validity of our result.
On properties of inner product type integral transformers
OMA-Vol. 4 (2020), Issue 2, pp. 160 – 169 Open Access Full-Text PDF
Benard Okelo
Abstract: In this paper, we give characterizations of certain properties of inner product type integral transformers. We first consider unitarily invariant norms and operator valued functions. We then give results on norm inequalities for inner product type integral transformers in terms of Landau inequality, Grüss inequality. Lastly, we explore some of the applications in quantum theory.
A holistic comparison between deep learning techniques to determine Covid-19 patients utilizing chest X-Ray images
EASL-Vol. 3 (2020), Issue 4, pp. 85 – 93 Open Access Full-Text PDF
Taki Hasan Rafi
Abstract: Novel coronavirus likewise called COVID-19 began in Wuhan, China in December 2019 and has now outspread over the world. Around 63 millions of people currently got influenced by novel coronavirus and it causes around 1,500,000 deaths. There are just about 600,000 individuals contaminated by COVID-19 in Bangladesh too. As it is an exceptionally new pandemic infection, its diagnosis is challenging for the medical community. In regular cases, it is hard for lower incoming countries to test cases easily. RT-PCR test is the most generally utilized analysis framework for COVID-19 patient detection. However, by utilizing X-ray image based programmed recognition can diminish the expense and testing time. So according to handling this test, it is important to program and effective recognition to forestall transmission to others. In this paper, author attempts to distinguish COVID-19 patients by chest X-ray images. Author executes various pre-trained deep learning models on the dataset such as Base-CNN, ResNet-50, DenseNet-121 and EfficientNet-B4. All the outcomes are compared to determine a suitable model for COVID-19 detection using chest X-ray images. Author also evaluates the results by AUC, where EfficientNet-B4 has 0.997 AUC, ResNet-50 has 0.967 AUC, DenseNet-121 has 0.874 AUC and the Base-CNN model has 0.762 AUC individually. The EfficientNet-B4 has achieved 98.86% accuracy.
On the entire Zagreb indices of the line graph and line cut-vertex graph of the subdivision graph
OMS-Vol. 4 (2020), Issue 1, pp. 470 – 475 Open Access Full-Text PDF
H. M. Nagesh, Girish V. R
Abstract: Let \(G=(V,E)\) be a graph. Then the first and second entire Zagreb indices of \(G\) are defined, respectively, as \(M_{1}^{\varepsilon}(G)=\displaystyle \sum_{x \in V(G) \cup E(G)} (d_{G}(x))^{2}\) and \(M_{2}^{\varepsilon}(G)=\displaystyle \sum_{\{x,y\}\in B(G)} d_{G}(x)d_{G}(y)\), where \(B(G)\) denotes the set of all 2-element subsets \(\{x,y\}\) such that \(\{x,y\} \subseteq V(G) \cup E(G)\) and members of \(\{x,y\}\) are adjacent or incident to each other. In this paper, we obtain the entire Zagreb indices of the line graph and line cut-vertex graph of the subdivision graph of the friendship graph.
Reverse Hermite-Hadamard’s inequalities using \(\psi\)-fractional integral
EASL-Vol. 3 (2020), Issue 4, pp. 75 – 84 Open Access Full-Text PDF
Tariq A. Aljaaidi, Deepak B. Pachpatte
Abstract: Our purpose in this paper is to use \(\psi-\)Riemann-Liouville fractional integral operator which is the fractional integral of any function with respect to another increasing function to establish some new fractional integral inequalities of Hermite-Hadamard, involving concave functions. Using the concave functions, we establish some new fractional integral
inequalities related to the Hermite-Hadamard type inequalities via \(\psi-\)Riemann-Liouville fractional integral operator.
inequalities related to the Hermite-Hadamard type inequalities via \(\psi-\)Riemann-Liouville fractional integral operator.
Boundary value problems for a class of stochastic nonlinear fractional order differential equations
OMA-Vol. 4 (2020), Issue 2, pp. 152 – 159 Open Access Full-Text PDF
McSylvester Ejighikeme Omaba, Louis O. Omenyi
Abstract: Consider a class of two-point Boundary Value Problems (BVP) for a stochastic nonlinear fractional order differential equation \(D^\alpha u(t)=\lambda\sqrt{I^\beta[\sigma^2(t,u(t))]}\dot{w}(t),\,\,00\) is a level of the noise term, \(\sigma:[0,1]\times\mathbb{R}\rightarrow\mathbb{R}\) is continuous, \(\dot{w}(t)\) is a generalized derivative of Wiener process (Gaussian white noise), \(D^\alpha\) is the Riemann-Liouville fractional differential operator of order \(\alpha\in (3,4)\) and \(I^\beta,\,\,\beta>0\) is a fractional integral operator. We formulate the solution of the equation via a stochastic Volterra-type equation and investigate its existence and uniqueness under some precise linearity conditions using contraction fixed point theorem. A case of the above BVP for a stochastic nonlinear second order differential equation for \(\alpha=2\) and \(\beta=0\) with \(u(0)=u(1)=0\) is also studied.
