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> Earthline Publishers, Madanambedu, Chittoor, Andhra Pradesh, India en-US Earthline Journal of Mathematical Sciences 2581-8147 <p><img src=""><br>This work is licensed under a&nbsp;<a href="" rel="license">Creative Commons Attribution 4.0 International License</a>.</p> 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) 2021-05-22 2021-05-22 7 1 1 23 10.34198/ejms.7121.123 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) 2021-05-22 2021-05-22 7 1 25 47 10.34198/ejms.7121.2547 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) 2021-05-28 2021-05-28 7 1 49 76 10.34198/ejms.7121.4976 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) 2021-06-02 2021-06-02 7 1 77 111 10.34198/ejms.7121.77111 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) 2021-06-21 2021-06-21 7 1 113 136 10.34198/ejms.7121.113136 Certain Subclass of Analytic Functions Defined by Wanas Operator <p>In present article, we introduce and study a certain family of analytic functions defined by Wanas operator in the open unit disk. We establish some important geometric properties for this family. Further we point out certain special cases for our results.</p> Timilehin Gideon Shaba Abbas Kareem Wanas Ismaila Omeiza Ibrahim Copyright (c) 2021-06-23 2021-06-23 7 1 137 144 10.34198/ejms.7121.137144 The New Results in Injective Modules <p>In this paper, we introduce and clarify a new presentation between the divisible module and the injective module. Also, we obtain some new results about them.</p> Samira Hashemi Feysal Hassani Rasul Rasuli Copyright (c) 2021-06-24 2021-06-24 7 1 145 159 10.34198/ejms.7121.145159 Fixed Point Theorems for the Alternate Interpolative Ciric-Reich-Rus Operator <p>In [1], the authors introduced the interpolative Ciric-Reich-Rus operator in Branciari metric space and obtained some fixed point theorems; in this work we present an alternate characterization of the interpolative Ciric-Reich-Rus operator in metric space, and obtain some fixed point theorems.</p> Clement Boateng Ampadu Copyright (c) 2021-07-10 2021-07-10 7 1 161 179 10.34198/ejms.7121.161179 Static Buckling Analysis of a Quadratic-Cubic Model Structure Using the Phase Plane Method and Method of Asymptotics <p>The exact and asymptotic analyses of the buckling of a quadratic-cubic model structure subjected to static loading are discussed. The governing equation is first solved using the phase plane method and next, using the method of asymptotics. In the asymptotic method, we discuss the possibilities of using regular perturbation method in asymptotic expansions of the relevant variables to get an approximate analytical solution to the problem. Finally, the two results are compared using numerical results obtained with the aid of Q-Basic codes. In the two methods discussed in this work, it is clearly seen that the static buckling loads decrease as the imperfection parameters increase. It is also observed that the static buckling loads obtained using the exact method are higher than those obtained using the method of asymptotics.</p> A. C. Osuji A. M. Ette J. U. Chukwuchekwa Copyright (c) 2021-07-13 2021-07-13 7 1 181 193 10.34198/ejms.7121.181193