Journal of the Nigerian Mathematical Society <p>Journal of the Nigerian Mathematical Society (JNMS)</p> <p>JNMS provides a means of communication and exchange of ideas among workers in mathematical sciences (mathematics, mathematical physics, statistics, computer science), and offers an effective method of bringing new results quickly to the public. By doing so the journal establishes an informal vehicle enabling the field of mathematical sciences to be understood in a broad sense. It will include theoretical and experimental results, and fundamental and practical research.<br /><br /></p> en-US (Professor J. A. Oguntuase) (ICTS) Sat, 22 Jun 2024 20:16:55 +0100 OJS 60 A NOVEL FIXED POINT ITERATION PROCESS APPLIED IN SOLVING DELAY DIFFERENTIAL EQUATIONS <p>In this paper we introduce a new four-step iteration process, called the Picard-Noor hybrid iterative process, and prove that this new iteration scheme converges to the unique fixed point of contraction operators. We then show that it converges faster than all of Picard, Mann, Noor, Krasnoselskii, Ishiwaka, Picard-Mann, Picard-Krosnoselskii, and Picard-Ishiwaka iteration processes with numerical examples visualized in graphs and tables to substantiate our claims. Data dependence result is proved and stability of the new process is shown. Our result is applied to the approximation of the solution of delay differential equations. Our results generalize and extend other results in literature.</p> Godwin Amechi Okeke, Henry, Victor, Oluwadara Copyright (c) 2024 Sat, 22 Jun 2024 00:00:00 +0100 ON APPROXIMATION METHODS FOR FIXED POINTS OF SET-VALUED PSEUDOCONTRACTIVE MAPPINGS <p>In this paper, it is our purpose to study implicit and explicit iterative methods for approximation of fixed point of multivalued pseudocontractive mappings in the setting of uniformly smooth real Banach space. Strong convergence of the sequences generated by these iterative algorithms are proved. The theorems obtained generalize and improve related results of several authors. Our method of proof is of independent interest.</p> Eric Ofoedu; Stanley C. Okoyeh, Adaeze N. Ofojebe, Grace N. Echezona Copyright (c) 2024 Sat, 22 Jun 2024 00:00:00 +0100 COMPUTATION OF THE GREEKS DELTA AND GAMMA OF ASIAN OPTION: A MALLIAVIN CALCULUS APPROACH <p>The challenges of pricing and hedging in financial market arise due to market uncertainties, quantified by sensitivities of underlying asseys, often represented using Greeks. Effective pricing and Hedging strategies are crucial for risk management, portfolio optimization and overall decision making in financial markets. These sensitivities which are represented by the Greeks are obtained with Malliavin calculus. The Malliavin integral calculus given by the Skorohod integral and the integration by part technique for stochastic variation were used to derive weight functions of the Greeks for Asian Option (AO). The weight functions were used to derive expressions for the Greeks which represent the sensitivities of the Asian option with respect to the parameters; price of the underlying asset at initial time $S_{0}$, and the volatility $\sigma$, respectively. <br />These sensitivities are important in financial market because it helps to monitor investment trajectory, it guide investor in decision making about the right time to cash in on their investment and to minimize risk.</p> Adeyemi Akeju, Ezekiel Ayoola Copyright (c) 2024 Sat, 22 Jun 2024 00:00:00 +0100 MULTIPLED BEST PROXIMITY POINTS FOR GENERALIZED CYCLIC ω-CONTRACTIONS <p>Non-self mappings from $A$ to $B$ do not necessarily have fixed points. However, when $A$ and $B$ are subsets of a distance type space, it is of interest to find elements as close as possible to their image. These elements are called best proximity points. In this paper, we prove the existence of multipled best proximity points of generalized cyclic contractions in metric spaces. The contractive condition is quite encompassing, generalizing, unifying and providing an erratum to existing related works in literature. An example is also given to illustrate the result.</p> Hallowed Olaoluwa, Johnson Olaleru Copyright (c) 2024 Sat, 22 Jun 2024 00:00:00 +0100 A TRIGONOMETRICALLY FITTED METHOD FOR SOLVING VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS. <p>A fifth-order block trigonometrically fitted<br>method is considered for the numerical solution of Volterra Integro-<br>Differential Equations (VIDEs). The proposed scheme is&nbsp;<br>constructed using a multistep collocation technique. The fundamental<br>&nbsp;properties such as zero-stability, and region of stability of<br>the proposed scheme are established, while its performance is<br>established through examples from recent scientific literature.</p> Ruth Olowe, Oluseye Akinfenwa, Ridwan Abdulganiy, Solomon Okunuga Copyright (c) 2024 Sat, 22 Jun 2024 00:00:00 +0100