Browsing by Author "Okeke, G.A."

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A novel fixed point iteration process applied in solving the Caputo type fractional differential equations in Banach spaces
(2024.01.01) Okeke, G.A.; Ugwuogor, C.I.; Alqahtani, R.T.; Kaplan, M.; Ahmed, W.E.
We introduce the modified Picard-Ishikawa hybrid iterative scheme and establish some strong convergence results for the class of asymptotically generalized phi-pseudocontractive mappings in the intermediate sense in Banach spaces and approximate the fixed point of this class of mappings via the newly introduced iteration scheme. We construct some numerical examples to support our results. Furthermore, we apply the Picard-Ishikawa hybrid iteration scheme in solving the nonlinear Caputo type fractional differential equations. Our results generalize, extend and unify several existing results in literature.
A novel iterative scheme for solving delay differential equations and third order boundary value problems via Green's functions
(2024.01.01) Okeke, G.A.; Udo, A.V.; Alqahtani, R.T.; Kaplan, M.; Ahmed, W.E.
In this paper, we constructed a novel fixed point iterative scheme called the Modified-JK iterative scheme. This iteration process is a modification of the JK iterative scheme. Our scheme converged weakly to the fixed point of a nonexpansive mapping and strongly to the fixed point of a mapping satisfying condition (E). We provided some examples to show that the new scheme converges faster than some existing iterations. Stability and data dependence results were proved for this iteration process. To substantiate our results, we applied our results to solving delay differential equations. Furthermore, the newly introduced scheme was applied in approximating the solution of a class of third order boundary value problems (BVPs) by embedding Green's functions. Moreover, some numerical examples were presented to support the application of our results to BVPs via Green's function. Our results extended and generalized other existing results in literature.
A novel iterative scheme for solving delay differential equations and third order boundary value problems via Green’s functions
(American Institute of Mathematical Sciences, 2024) Okeke, G.A.; Udo, A.V.; Alqahtani, R.T.; Kaplan, M.; Ahmed, W.E.
In this paper, we constructed a novel fixed point iterative scheme called the Modified-JK iterative scheme. This iteration process is a modification of the JK iterative scheme. Our scheme converged weakly to the fixed point of a nonexpansive mapping and strongly to the fixed point of a mapping satisfying condition (E). We provided some examples to show that the new scheme converges faster than some existing iterations. Stability and data dependence results were proved for this iteration process. To substantiate our results, we applied our results to solving delay differential equations. Furthermore, the newly introduced scheme was applied in approximating the solution of a class of third order boundary value problems (BVPs) by embedding Green’s functions. Moreover, some numerical examples were presented to support the application of our results to BVPs via Green’s function. Our results extended and generalized other existing results in literature.