• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.233-247
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• 2022

In the present manuscript, we employ the concepts of Θ-map and Φ-map to define a strong (𝜃, 𝜙)s-contraction of a map f in a b-metric space (M, d_b). Then we prove and derive many fixed point theorems as well as we provide an example to support our main result. Moreover, we utilize our results to obtain many results in the settings of metric and G-metric spaces. Our results improve and modify many 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.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.1-7
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• 2002

For A bounded subset G of a metric Space (X,d) and $\chi \in X$, let $f_{G}$ be the real-valued function on X defined by $f_{G}$($\chi$)=sup{$d (\chi, g)\in:G$}, and $F(G,\chi)$={$z \in X:sup_{g \in G}d(g,z)=sup_{g \in G}d(g,\chi)+d(\chi,z)$}. In this paper we discuss some properties of the map $f_G$ and of the set $ F(G, \chi)$ in convex metric spaces. A sufficient condition for an element of a convex metric space X to lie in $ F(G, \chi)$ is also given in this pope.

• 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.

• 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].

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.529-539
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• 2021

The purpose of this paper is to prove some fixed point theorems using (𝜓, 𝜑)-contractions via the concept of C-class functions in G_b-metric spaces. Moreover, an example is presented to illustrate the validity of our results.

• The Pure and Applied Mathematics
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• v.20 no.1
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• pp.11-23
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• 2013

In this paper, we obtain a common fixed point theorem for multivalued mappings in a complete Menger $\mathcal{L}$-fuzzy metric space. $\mathcal{L}$-fuzzy metric space is a generalization of fuzzy metric spaces and intuitionistic fuzzy metric spaces. We extend and generalize the results of Kubiaczyk and Sharma [24], Sharma, Kutukcu and Rathore [34].

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.177-195
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• 2021

In this paper, we introduce the modification of a generalized (Ψ, L)-weak contraction and we prove some coincidence point results for self-mappings G, T and S, and some fixed point results for some maps by using a (c)-comparison function and a comparison function in the sense of a b-metric space.

• 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.277-288
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• 2019

The main objective of this article is to establish some coincidence point theorem for g-non-decreasing mappings under contraction mapping principle on a partially ordered metric space. Furthermore, we constitute multidimensional results as a simple consequences of our unidimensional coincidence point theorem. Our results improve and generalize various known results.