Journal of the Nigerian Mathematical Society

A NOVEL FIXED POINT ITERATION PROCESS APPLIED IN SOLVING DELAY DIFFERENTIAL EQUATIONS

Godwin Amechi Okeke — 2024-06-22

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.

ON APPROXIMATION METHODS FOR FIXED POINTS OF SET-VALUED PSEUDOCONTRACTIVE MAPPINGS

Eric Ofoedu — 2024-06-22

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.

COMPUTATION OF THE GREEKS DELTA AND GAMMA OF ASIAN OPTION: A MALLIAVIN CALCULUS APPROACH

Adeyemi Akeju — 2024-06-22

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.
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.

MULTIPLED BEST PROXIMITY POINTS FOR GENERALIZED CYCLIC ω-CONTRACTIONS

Hallowed Olaoluwa — 2024-06-22

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.

A TRIGONOMETRICALLY FITTED METHOD FOR SOLVING VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS.

Ruth Olowe — 2024-06-22

A fifth-order block trigonometrically fitted
method is considered for the numerical solution of Volterra Integro-
Differential Equations (VIDEs). The proposed scheme is
constructed using a multistep collocation technique. The fundamental
properties such as zero-stability, and region of stability of
the proposed scheme are established, while its performance is
established through examples from recent scientific literature.