Earthline Journal of Mathematical Sciences <p style="text-align: justify;">The Earthline Journal of Mathematical Sciences (e-ISSN: 2581-8147) is a peer-reviewed international journal devoted to publishing original research papers containing substantial contributions in any direction of Pure and Applied Mathematics, Theoretical and Applied Statistics, Theoretical Computer Science, Mathematical Physics, Mathematical Chemistry, Mathematical Modelling, Mathematical Biology. Applications of Mathematics in Finance and Economics are also welcome.</p> en-US <p><img src=""><br>This work is licensed under a&nbsp;<a href="" rel="license">Creative Commons Attribution 4.0 International License</a>.</p> (Fabiola Malowney) (K. Jhansi Rani) OJS 60 Strongly log-biconvex Functions and Applications <p>In this paper, we consider some new classes of log-biconvex functions. Several properties of the log-biconvex functions are studied. We also discuss their relations with convex functions. Several interesting results characterizing the log-biconvex functions are obtained. New parallelogram laws are obtained as applications of the strongly log-biconvex functions. Optimality conditions of differentiable strongly log-biconvex&nbsp; are characterized by a class of bivariational inequalities. Results obtained in this paper can be viewed as significant improvement of previously known results.</p> Muhammad Aslam Noor, Khalida Inayat Noor Copyright (c) Sat, 22 May 2021 00:00:00 +0000 On the Convergence of LHAM and its Application to Fractional Generalised Boussinesq Equations for Closed Form Solutions <p>By fractional generalised&nbsp; Boussinesq equations we mean equations of the form</p> <p><img src="/public/site/images/ejms/2021-05-22_13_44_47-Adobe_Acrobat_Professional_-_[EJMS070120212547.pdf]_1.png"></p> <p>where <img src="/public/site/images/ejms/2021-05-22_13_45_11-Adobe_Acrobat_Professional_-_[EJMS070120212547.pdf]_.png"> is a differentiable function and <img src="/public/site/images/ejms/2021-05-22_13_45_24-Adobe_Acrobat_Professional_-_[EJMS070120212547.pdf]_.png"> (to ensure nonlinearity). In this paper we lay emphasis on the cubic Boussinesq and Boussinesq-like equations of fractional order and we apply the Laplace homotopy analysis method (LHAM) for their rational and solitary wave solutions respectively. It is true that nonlinear fractional differential equations are often difficult to solve for their <em>exact</em> solutions and this single reason has prompted researchers over the years to come up with different methods and approach for their <em>analytic approximate</em> solutions. Most of these methods require huge computations which are sometimes complicated and a very good knowledge of computer aided softwares (CAS) are usually needed. To bridge this gap, we propose a method that&nbsp; requires no linearization, perturbation or any particularly restrictive assumption that can be easily used to solve strongly nonlinear fractional differential equations by hand and simple computer computations with a very quick run time. For the closed form solution, we set <img src="/public/site/images/ejms/2021-05-22_13_45_41-Adobe_Acrobat_Professional_-_[EJMS070120212547.pdf]_.png">&nbsp;for each of the solutions and our&nbsp; results&nbsp; coincides with those of&nbsp; others in the literature.</p> S. O. Ajibola, E. O. Oghre, A. G. Ariwayo, P. O. Olatunji Copyright (c) Sat, 22 May 2021 00:00:00 +0000 Certain Properties of a Generalized Class of Analytic Functions Involving Some Convolution Operator <p>We use the concept of convolution to introduce and study the properties of a unified family <sub><img src="/public/site/images/ejms/2021-05-28_21_54_19-Adobe_Acrobat_Professional_-_[EJMS070120214976.pdf]_1.png"></sub>&nbsp;consisting of uniformly <em>k</em>-starlike and <em>k</em>-convex functions of complex order <sub><img src="/public/site/images/ejms/2021-05-28_21_54_48-Adobe_Acrobat_Professional_-_[EJMS070120214976.pdf]_.png"></sub> and type <sub><img src="/public/site/images/ejms/2021-05-28_21_55_03-Adobe_Acrobat_Professional_-_[EJMS070120214976.pdf]_.png"></sub> The family <sub><img src="/public/site/images/ejms/2021-05-28_21_55_28-Adobe_Acrobat_Professional_-_[EJMS070120214976.pdf]_.png"></sub> is a generalization of several other families of analytic functions available in literature. Apart from discussing the coefficient bounds, sharp radii estimates, extreme points and the subordination theorem for this family, we settle down the Silverman’s conjecture for integral means inequality. Moreover, invariance of this family under certain well-known integral operators is also established in this paper. Some previously known results are obtained as special cases.</p> Faroze Ahmad Malik, Nusrat Ahmed Dar, Chitaranjan Sharma Copyright (c) Fri, 28 May 2021 00:00:00 +0000 Notes on Binomial Transform of the Generalized Narayana Sequence <p>In this paper, we define the binomial transform of the generalized Narayana sequence and as special cases, the binomial transform of the Narayana, Narayana-Lucas, Narayana-Perrin sequences will be introduced. We investigate their properties in details.</p> Yüksel Soykan Copyright (c) Wed, 02 Jun 2021 00:00:00 +0000 Influence Function and Bootstrap Methods of Estimating the Standard Errors of the Estimators of Mixture Exponential Distribution Parameter <p>This work estimated the standard error of the maximum likelihood estimator (MLE) and the robust estimators of the exponential mixture parameter (θ) using the influence function and the bootstrap approaches. Mixture exponential random samples of sizes 10, 15, 20, 25, 50, and 100 were generated using 3 mixture exponential models at 2%, 5% and 10% contamination levels. The selected estimators namely: mean, median, alpha-trimmed mean, Huber M-estimate and their standard errors (<em>T<sub>n</sub></em> ) were estimated using the two approaches at the indicated sample sizes and contamination levels. The results were compared using the coefficient of variation, confidence interval and the asymptotic relative efficiency of <em>T<sub>n</sub></em> in order to find out which approach yields the more reliable, precise and efficient estimate of <em>T<sub>n</sub></em>. The results of the analysis show that the two approaches do not equally perform at all conditions. From the results, the bootstrap method was found to be more reliable and efficient method of estimating the standard error of the arithmetic mean at all sample sizes and contamination levels. In estimating the standard error of the median, the influence function method was found to be more effective especially when the sample size is small and yet contamination is high. The influence function based approach yielded more reliable, precise and efficient estimates of the standard errors of the alpha-trimmed mean and the Huber M-estimate for all sample sizes and levels of contamination although the reliability of the bootstrap method improved better as sample size increased to 50 and above. All simulations and analysis were carried out in R programming language.</p> J. I. Udobi, G. A. Osuji, S. I. Onyeagu, H. O. Obiora-Ilouno Copyright (c) Mon, 21 Jun 2021 00:00:00 +0000