<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we use Lyapunov’s second method, by constructing a complete Lyapunov functional, sufficient conditions which guarantee existence and uniqueness of a periodic solution, uniform asymptotic stability of the trivial solution and uniform ultimate boundedness of solutions of Eq. (2). New results are obtained and proved, an example is given to illustrate the theoretical analysis in the work and to test the effectiveness of the method employed. The results obtained in this investigation extend many existing and exciting results on nonlinear third order delay differential equations.</abstract>

Existence and uniqueness of a periodic solution to certain third order nonlinear delay differential equation with multiple deviating arguments

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we consider the performance evaluation of two retrial queueing system. Customers arrive to the system, if upon arrival, the queue is full, the new arriving customers either move into one of the orbits, from which they make a new attempts to reach the primary queue, until they find the server idle or balk and leave the system, these later, and after getting a service may comeback to the system requiring another service. So, we derive for this system, the joint distribution of the server state and retrial queue lengths. Then, we give some numerical results that clarify the relationship between the retrials, arrivals, balking rates, and the retrial queue length.</abstract>

Performance evaluation of two Markovian retrial queueing model with balking and feedback

<abstract xmlns="http://www.w3.org/1999/xhtml">In the present paper, we obtain a new result on fixed point theorem for four metric spaces. Here we choose continuous mappings. In fact our result is the generalization of many results of fixed point theorem on two and three metric spaces. We also give some illustrative examples to justify our result.</abstract>

Related fixed point theorem for four complete metric spaces

<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper we prove some properties of the indefinite Lorentzian para-Sasakian manifolds. Section 1 is introductory. In Section 2 we define D-totally geodesic and D⊥-totally geodesic contact CRsubmanifolds of an indefinite Lorentzian para-Sasakian manifold and deduce some results concerning such a manifold. In Section 3 we state and prove some results on mixed totally geodesic contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold. Finally, in Section 4 we obtain a result on the anti-invariant distribution of totally umbilic contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold.</abstract>

University Department of Mathematics Kolkata-700032, India

Jadavpur University Department of Mathematics Kolkata-700032, India

Contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold

<abstract xmlns="http://www.w3.org/1999/xhtml">The Nelder-Mead simplex method is a widespread applied numerical optimization method with a vast number of practical applications, but very few mathematically proven convergence properties. The original formulation of the algorithm is stated in Rn using terms of Euclidean geometry. In this paper we introduce the idea of a hyperbolic variant of this algorithm using the Poincaré disk model of the Bolyai- Lobachevsky geometry. We present a few basic properties of this method and we also give a Matlab implementation in 2 and 3 dimensions</abstract>

A hyperbolic variant of the Nelder–Mead simplex method in low dimensions

<abstract xmlns="http://www.w3.org/1999/xhtml">In the paper, with the aid of weighted sharing method we study the problems of meromorphic functions that share fixed points (or a nonzero finite value) and poles with finite weights. The results of the paper improve some recent results due to Y. H. Cao and X. B. Zhang [Journal of Inequalities and Applications, 2012:100].</abstract>

Meromorphic functions sharing fixed points and poles with finite weights

<abstract xmlns="http://www.w3.org/1999/xhtml">By using the principle of differential subordination, we introduce subclass of p-valent meromorphic functions involving convolution and investigate various properties for this subclass. We also indicate relevant connections of the various results presented in this paper with the obtained results in earlier works.</abstract>

Fayoum University Faculty of Science Department of Mathematics Fayoum 63514, Egypt

Mansoura University Faculty of Science Department of Mathematics Mansoura 35516, Egypt

Some applications of differential subordination to certain subclass of p-valent meromorphic functions involving convolution

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Volume 15 (2023): Issue 2 (December 2023)

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Acta Universitatis Sapientiae, Mathematica

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