Austine Efut Ofem, Unwana Effiong Udofia, Donatus Ikechi Igbokwe, “A robust iterative approach for solving nonlinear Volterra delay integro-differential equations”, Ural Math. J., 7:2 (2021), 59

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Ural Mathematical Journal, 2021, Volume 7, Issue 2, Pages 59–85
DOI: https://doi.org/10.15826/umj.2021.2.005 (Mi umj150)

This article is cited in 16 scientific papers (total in 16 papers)

A robust iterative approach for solving nonlinear Volterra delay integro-differential equations

Austine Efut Ofem^a, Unwana Effiong Udofia^b, Donatus Ikechi Igbokwe^c

^a Department of Mathematics, University of Uyo
^b Department of Mathematics and Statistics, Akwa Ibom State University
^c Department of Mathematics, Michael Okpara University of Agriculture

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DOI: https://doi.org/10.15826/umj.2021.2.005

Abstract: This paper presents a new iterative algorithm for approximating the fixed points of multivalued generalized

α

$\alpha$ -nonexpansive mappings. We study the stability result of our new iterative algorithm for a larger concept of stability known as weak

w^{2}

$w^2$ –stability. Weak and strong convergence results of the proposed iterative algorithm are also established. Furthermore, we show numerically that our new iterative algorithm outperforms several known iterative algorithms for multivalued generalized

α

$\alpha$ -nonexpansive mappings. Again, as an application, we use our proposed iterative algorithm to find the solution of nonlinear Volterra delay integro-differential equations. Finally, we provide an illustrative example to validate the mild conditions used in the result of the application part of this study. Our results improve, generalize and unify several results in the existing literature.

Keywords: Banach space, uniformly convex Banach space, multivalued generalized

α

$\alpha$ -nonexpansive mapping, convergence, nonlinear Volterra delay integro-differential equations.

Bibliographic databases:

Document Type: Article

Language: English

Citation: Austine Efut Ofem, Unwana Effiong Udofia, Donatus Ikechi Igbokwe, “A robust iterative approach for solving nonlinear Volterra delay integro-differential equations”, Ural Math. J., 7:2 (2021), 59–85

Citation in format AMSBIB

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\by Austine~Efut~Ofem, Unwana~Effiong~Udofia, Donatus~Ikechi~Igbokwe

\paper A robust iterative approach for solving nonlinear Volterra delay integro-differential equations

\jour Ural Math. J.

\yr 2021

\vol 7

\issue 2

\pages 59--85

\mathnet{http://mi.mathnet.ru/umj150}

\crossref{https://doi.org/10.15826/umj.2021.2.005}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR4358914}

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Linking options:

https://www.mathnet.ru/eng/umj150

https://www.mathnet.ru/eng/umj/v7/i2/p59

This publication is cited in the following 16 articles:

Dimplekumar Chalishajar, Meena Somasundaram, Panayappan Sethuraman, “Analyticity of Weighted Composition Semigroups on the Space of Holomorphic Functions”, Bull. Iran. Math. Soc., 51:1 (2025)
James Abah Ugboh, Joseph Oboyi, Mfon Okon Udo, Hossam A. Nabwey, Austine Efut Ofem, Ojen Kumar Narain, “On a Faster Iterative Method for Solving Fractional Delay Differential Equations in Banach Spaces”, Fractal Fract, 8:3 (2024), 166 $https://doi.org/10.3390/fractalfract8030166$
Austine Efut Ofem, Jacob Ashiwere Abuchu, Godwin Chidi Ugwunnadi, Hossam A. Nabwey, Abubakar Adamu, Ojen Kumar Narain, “Double inertial steps extragadient-type methods for solving optimal control and image restoration problems”, MATH, 9:5 (2024), 12870
Ahmed Alamer, Faizan Ahmad Khan, “Boyd-Wong type functional contractions under locally transitive binary relation with applications to boundary value problems”, MATH, 9:3 (2024), 6266
Austine Efut Ofem, Jacob Ashiwere Abuchu, Godwin Chidi Ugwunnadi, Ojen Kumar Narain, Hassen Aydi, Choonkil Park, “A MIXED-TYPE PICARD-S ITERATIVE METHOD FOR ESTIMATING COMMON FIXED POINTS IN HYPERBOLIC SPACES”, jaac, 14:3 (2024), 1302
K. Alsa'di,, N. M. A. Nik Long, Z. K. Eshkuvatov, “Theoretical and Numerical Studies of Fractional Volterra-Fredholm Integro-Differential Equations in Banach Space”, MJMS, 18:3 (2024), 469
Austine Efut Ofem, Hüseyin Işik, Godwin Chidi Ugwunnadi, Reny George, Ojen Kumar Narain, “Approximating the solution of a nonlinear delay integral equation by an efficient iterative algorithm in hyperbolic spaces”, MATH, 8:7 (2023), 14919
Austine Efut Ofem, Jacob Ashiwere Abuchu, Hossam A. Nabwey, Godwin Chidi Ugwunnadi, Ojen Kumar Narain, “On Bilevel Monotone Inclusion and Variational Inequality Problems”, Mathematics, 11:22 (2023), 4643
M. O. Udo, A. E. Ofem, J. Oboyi, C. F. Chikwe, S. E. Ekoro, F. A. Adie, “Some common fixed point results for three total asymptotically pseudocontractive mappings”, J Anal, 31:3 (2023), 2005
S. Behera, S. Saha Ray, “A Novel Numerical Scheme Based on Müntz–Legendre Wavelets for Solving Pantograph Volterra Delay-Integro-Differential Equations”, Mediterr. J. Math., 20:1 (2023)
Austine Efut Ofem, Mfon Okon Udo, Oboyi Joseph, Reny George, Chukwuka Fernando Chikwe, “Convergence Analysis of a New Implicit Iterative Scheme and Its Application to Delay Caputo Fractional Differential Equations”, Fractal Fract, 7:3 (2023), 212 $https://doi.org/10.3390/fractalfract7030212$
Marimuthu Mohan Raja, Velusamy Vijayakumar, Anurag Shukla, Kottakkaran Sooppy Nisar, Wedad Albalawi, Abdel-Haleem Abdel-Aty, “A new discussion concerning to exact controllability for fractional mixed Volterra-Fredholm integrodifferential equations of order ${r} \in (1, 2)$ with impulses”, MATH, 8:5 (2023), 10802
Danish Ali, Shahbaz Ali, Darab Pompei-Cosmin, Turcu Antoniu, Abdullah A. Zaagan, Ali M. Mahnashi, “A Quicker Iteration Method for Approximating the Fixed Point of Generalized α-Reich-Suzuki Nonexpansive Mappings with Applications”, Fractal Fract, 7:11 (2023), 790 $https://doi.org/10.3390/fractalfract7110790$
Godwin Amechi Okeke, Austine Efut Ofem, Thabet Abdeljawad, Manar A. Alqudah, Aziz Khan, “A solution of a nonlinear Volterra integral equation with delay via a faster iteration method”, MATH, 8:1 (2023), 102
Austine Efut Ofem, Aftab Hussain, Oboyi Joseph, Mfon Okon Udo, Umar Ishtiaq, Hamed Al Sulami, Chukwuka Fernando Chikwe, “Solving Fractional Volterra–Fredholm Integro-Differential Equations via A** Iteration Method”, Axioms, 11:9 (2022), 470
Austine Efut Ofem, Jacob Ashiwere Abuchu, Reny George, Godwin Chidi Ugwunnadi, Ojen Kumar Narain, “Some New Results on Convergence, Weak w2-Stability and Data Dependence of Two Multivalued Almost Contractive Mappings in Hyperbolic Spaces”, Mathematics, 10:20 (2022), 3720

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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