• The Pure and Applied Mathematics
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• v.21 no.1
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• pp.23-38
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• 2014

In this paper, we introduce the concept of w¡compatibility and weakly commutativity for hybrid pair of mappings $F:X{\times}X{\times}X{\rightarrow}2^X$ and $g:X{\rightarrow}X$ and establish a common tripled fixed point theorem under generalized nonlinear contraction. An example is also given to validate our result. We improve, extend and generalize various known results.

• The Pure and Applied Mathematics
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• v.23 no.1
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• pp.35-51
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• 2016

We establish coincidence point theorem for g-nondecreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings F, G : X² → X by using obtained coincidence point results. Furthermore, an example is also given to demonstrate the degree of validity of our hypothesis. Our results generalize, modify, improve and sharpen several well-known results.

• East Asian mathematical journal
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• v.32 no.3
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• pp.333-354
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• 2016

We present coincidence point theorem for g-non-decreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings $F,G:X^2{\rightarrow}X$ by using obtained coincidence point results. Furthermore, an example and an application to integral equation are also given to show the usability of obtained results. Our results generalize, modify, improve and sharpen several well-known results.

• The Pure and Applied Mathematics
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• v.25 no.4
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• pp.279-295
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• 2018

We study the existence and uniqueness of fixed point for isotone mappings of any number of arguments under Geraghty-type contraction on a complete metric space endowed with a partial order. As an application of our result we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. Our results generalize, extend and unify several classical and very recent related results in the literature in metric spaces.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.395-405
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• 2023

In this manuscript, we establish the concept of 𝓗(ω, θ)-contraction which based on modified ω distance mappings which introduced by Alegre and Marin [4] in 2016 and 𝓗 simulation functions which introduced by Bataihah et.al. [14] in 2020 and we employ our contraction to prove the existence and uniqueness some new fixed point results. On the other hand, we create some examples and an application to show the importance of our results.

• East Asian mathematical journal
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• v.26 no.3
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• pp.337-350
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• 2010

Strong convergence theorem of the explicit viscosity iterative scheme involving the sunny nonexpansive retraction for nonexpansive nonself-mappings is established in a reflexive and strictly convex Banach spaces having a weakly sequentially continuous duality mapping. The main result improves the corresponding result of [19] to the more general class of mappings together with certain different control conditions.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1901-1910
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• 2015

In the present paper, considering the Jleli and Samet's technique we give many fixed point results for multivalued mappings on complete metric spaces without using the Pompeiu-Hausdorff metric. Our results are real generalization of some related fixed point theorems including the famous Feng and Liu's result in the literature. We also give some examples to both illustrate and show that our results are proper generalizations of the mentioned theorems.

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.85-98
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• 2009

Strong convergence theorems on viscosity approximation methods for finite nonexpansive mappings are established in Banach spaces. The main theorem generalize the corresponding result of Kim and Xu [10] to the viscosity approximation method for finite nonexpansive mappings in a reflexive Banach space having a uniformly Gateaux differentiable norm. Our results also improve the corresponding results of [7, 8, 19, 20].

• Journal of applied mathematics & informatics
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• v.42 no.4
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• pp.749-759
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• 2024

In this manuscript, we formulate the notion of Ω(H, θ)-contraction on a self mapping f : W → W, this contraction based on the concept of Ω-distance mappings equipped on G-metric spaces together with the concept of H-simulation functions and the class of Θ-functions, we employ our new contraction to unify the existence and uniqueness of some new fixed point results. Moreover, we formulate a numerical example and a significant application to show the novelty of our results; our application is based on the significant idea that the solution of an equation in a certain condition is similar to the solution of a fixed point equation. We are utilizing this idea to prove that the equation, under certain conditions, not only has a solution as the Intermediate Value Theorem says but also that this solution is unique.

• Journal of the Korean Mathematical Society
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• v.19 no.2
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• pp.135-141
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• 1983