• The Pure and Applied Mathematics
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• v.30 no.3
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• pp.309-336
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• 2023

We establish some common fixed point theorems satisfying weak ψ - ϕ contraction on partially ordered non-Archimedean fuzzy metric spaces. By using this results we show the existence of fixed point on the domain of words and apply this approach to deduce the existence of solution for some recurrence equations associated to the analysis of Quicksort algorithms and divide and Conquer algorithms, respectively and also give an example to show the usefulness of our hypothesis. Our results generalize, extend and improve several well-known results of the existing literature in fixed point theory.

• Nuclear Engineering and Technology
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• v.49 no.5
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• pp.1095-1099
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• 2017

A fission source can act as a stabilization element in coupled Monte Carlo simulations. We have observed this while studying numerical instabilities in nonlinear steady-state simulations performed by a Monte Carlo criticality solver that is coupled to a xenon feedback solver via fixed-point iteration. While fixed-point iteration is known to be numerically unstable for some problems, resulting in large spatial oscillations of the neutron flux distribution, we show that it is possible to stabilize it by reducing the number of Monte Carlo criticality cycles simulated within each iteration step. While global convergence is ensured, development of any possible numerical instability is prevented by not allowing the fission source to converge fully within a single iteration step, which is achieved by setting a small number of criticality cycles per iteration step. Moreover, under these conditions, the fission source may converge even faster than in criticality calculations with no feedback, as we demonstrate in our numerical test simulations.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.773-785
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• 2012

In this paper, we establish sufficient conditions for the existence and uniqueness of solutions to a general class of three-point boundary value problems for a coupled system of nonlinear fractional differential equations. The differential operator is taken in the Caputo fractional derivatives. By using Green's function, we transform the derivative systems into equivalent integral systems. The existence is based on Schauder fixed point theorem and contraction mapping principle. Finally, some examples are given to show the applicability of our results.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.221-233
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• 2016

The present paper proposes a new monotone iteration method for existence as well as approximation of the coupled solutions for a coupled periodic boundary value problem of first order ordinary nonlinear differential equations. A new hybrid coupled fixed point theorem involving the Dhage iteration principle is proved in a partially ordered normed linear space and applied to the coupled periodic boundary value problems for proving the main existence and approximation results of this paper. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related differential equations under some suitable mixed hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.993-1005
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• 2013

In this paper, to include more generalized cases, the authors present a modified concept for the tripled and quadruple fixed point of the mixed monotone mappings. Also, they investigate the existence and uniqueness of fixed point of the ordered monotone operator with the Matkowski contractive conditions in the partial ordered metric spaces. As the direct consequences, the existence of coupled fixed point, tripled fixed point and quadruple fixed point are explored at the common framework and some previous results in [T. G. Bhaskar and V. Lakshmikan-tham, Fixed point theory in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379-1393; V. Berinde and M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011), no. 15, 4889-4897; E. Karapinar and N. V. Luong, Quadruple fixed point theorems for nonlinear contractions, Computers and Mathematics with Applications (2012), doi:10.1016/j.camwa.2012.02061] are improved. Finally, some fixed point theorems are proved.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1189-1207
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• 2014

A partial metric, also called a nonzero self-distance, is motivated by experience from computer science. Besides a lot of properties of partial metric analogous to those of metric, fixed point theorems in partial metric spaces have been studied recently. We establish several kinds of extended fixed point theorems in ordered partial metric spaces with higher dimension under generalized notions of mixed monotone mappings.

• The Pure and Applied Mathematics
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• v.30 no.3
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• pp.249-267
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• 2023

This manuscript is divided into three segments. In the first segment, we prove a unique common fixed point theorem satisfying generalized weak contraction on partially ordered metric spaces and also give an example to support our results presented here. In the second segment of the article, some common coupled fixed point results are derived from our main results. In the last segment, we investigate the solution of integral equation as an application. Our results generalize, extend and improve several well-known results of the existing literature.

• The Pure and Applied Mathematics
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• v.30 no.4
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• pp.443-461
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• 2023

In this paper, we establish some common fixed point theorems satisfying contraction mapping principle on partially ordered non-Archimedean fuzzy metric spaces and also derive some coupled fixed point results with the help of established results. We investigate the solution of integral equation and also give an example to show the applicability of our results. These results generalize, improve and fuzzify several well-known results in the recent literature.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.1-14
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• 2018

In this paper, we prove the existence, uniqueness and stability of solution for some nonlinear functional-integral equations by using generalized coupled Lipschitz condition. We prove a fixed point theorem to obtain the mentioned aim in Banach space $X=C([a,b],{\mathbb{R}})$. As application we study some volterra integral equations with linear, nonlinear and single kernel.

• East Asian mathematical journal
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• v.39 no.1
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• pp.43-50
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• 2023

This paper is concerned with the existence of positive solutions to the second order differential systems with strongly coupled integral boundary value conditions. The fixed point index theorems are used for the main results.