• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.581-600
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• 2021

In this paper we obtain a unique common fixed point theorem for four self-maps which are involved in (𝜙, 𝜓)-weak contraction of a partially ordered b-metric space. The necessary condition has been given to a space for the existence of an unique common fixed of the maps. And our work changed conditions and nonlinear contraction, and search for the unique common fixed point of the maps.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.117-128
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• 2012

Using the concept of a g-monotone mapping we prove some common fixed point theorems for g-non-decreasing mappings which satisfy some generalized nonlinear contractions in partially ordered complete quasi b-metric spaces. The new theorems are generalizations of very recent fixed point theorems due to L. Ciric, N. Cakic, M. Rojovic, and J. S. Ume, [Monotone generalized nonlinear contractions in partailly ordered metric spaces, Fixed Point Theory Appl. (2008), article, ID-131294] and R. P. Agarwal, M. A. El-Gebeily, and D. O'Regan [Generalized contractions in partially ordered metric spaces, Appl. Anal. 87 (2008), 1-8].

• The Pure and Applied Mathematics
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• v.26 no.4
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• pp.289-303
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• 2019

We study the existence and uniqueness of fixed point for isotone mappings of any number of arguments under Mizoguchi-Takahashi 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 integral equation. The results we obtain generalize, extend and unify several very recent related results in the literature.

• 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.