• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.557-570
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• 2023

The conceptions of generalized b-metric spaces or G_b-metric spaces and a generalized Ω-distance mappings play a key role in proving many important theorems in existence and uniqueness of fixed point theory. In this manuscript, we establish a new type of contraction namely, Ω_b(𝓗, 𝜃, s)-contraction, this contraction based on the concept of a generalized Ω-distance mappings which established by Abodayeh et.al. in 2017 together with the concept of 𝓗-simulation functions which established by Bataihah et.al [10] in 2020. By utilizing this new notion we prove new results in existence and uniqueness of fixed point. On the other hand, examples and application were established to show the importance of our results.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.65-74
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• 2017

In this paper, we establish a unique common fixed point theorem for T-contraction of two self maps on generalized cone b-metric spaces with solid cone. The result of this paper improves and generalizes several well-known results in the literature. Two examples are also given to support the result.

• 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].

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.375-387
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• 2017

In this paper, we prove some coincidence point theorems involving ${\varphi}-contraction$ in ordered partial metric spaces. We also extend newly introduced notion of g-comparability of a pair of maps for linear contraction in ordered metric spaces to non-linear contraction in ordered partial metric spaces. Thus, our results extend, modify and generalize some recent well known coincidence point theorems of ordered metric spaces.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1147-1170
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• 2022

In this paper, we introduce a new class of mappings called the generalized orthogonal F-Suzuki contraction for a family of multivalued mappings in the setup of orthogonal b-metric spaces. We established the existence of some common fixed point results without using any commutativity condition for this new class of mappings in orthogonal b-metric spaces. Moreover, we illustrate and support these common fixed point results with example. The results obtained in this work generalize and extend some recent and classical related results in the existing literature.

• The Pure and Applied Mathematics
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• v.27 no.4
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• pp.207-229
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• 2020

We establish fixed point and multidimensional fixed point results satisfying generalized (𝜓, 𝜃, 𝜑)-contraction on partially ordered non-Archimedean fuzzy metric spaces. By using this result we obtain the solution for periodic boundary value problems and give an example to show the degree of validity of our hypothesis. Our results generalize, extend and modify several well-known results in the literature.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.885-899
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• 2000

We obtain generalized versions of the Fan-Browder fixed point theorem for G-convex spaces. We define the class B of better admissible multimaps on G-convex spaces and show that any closed compact map in b fro ma locally G-convex uniform space into itself has a fixed point.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1363-1371
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• 2016

This paper is concerned with best proximity points for multimaps in normed spaces and in hyperconvex metric spaces. Using the generalized KKM theorem, we deduce new best proximity pair theorems for a family of multimaps with unionly open fibers in normed spaces. And we prove a new best proximity point theorem for quasi-lower semicontinuous multimaps in hyperconvex metric spaces.

• Korean Journal of Mathematics
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• v.31 no.2
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• pp.123-131
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• 2023

In this paper, we prove existence of best proximity points for 2-convex contraction, 2-sided contraction, and M-weakly cyclic 2-convex contraction mappings in the setting of complete strongly regular generalized modular metric spaces that generalize many results in the literature.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.485-500
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• 2014

In this paper, we establish coupled fixed point theorems for mixed monotone mappings satisfying nonlinear contraction involving a pair of altering distance functions in ordered G-metric spaces. Via presented theorems we extend and generalize the results of Harjani et al. [J. Harjani, B. L$\acute{o}$pez and K. Sadarangani, Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Anal. 74 (2011) 1749-1760] and Choudhury and Maity [B.S. Choudhury and P. Maity, Coupled fixed point results in generalized metric spaces. Math. Comput. Model. 54 (2011), 73-79].