• East Asian mathematical journal
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• 제16권2호
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• pp.175-181
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• 2000

In this paper we show fixed point theorems related with the diameter of orbit on metric spaces. The results presented in this paper extend, improve and unify the results of $Heged\"{u}s$ [1], Kim, Kim, Leem and Ume [2], Kim and Leem [3], Ohta and Nikaido [4] and $Taskovi\'{c}$ [5].

• East Asian mathematical journal
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• 제27권3호
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• pp.273-288
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• 2011

In this paper, we prove some common fixed point theorem for two nonlinear mappings in complete $\mathcal{M}$-fuzzy metric spaces. Our main results improved versions of several fixed point theorems in complete fuzz metric spaces.

• 대한수학회논문집
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• 제24권4호
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• pp.565-579
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• 2009

In this paper, we give some new fixed point theorems for contractive type mappings in intuitionistic fuzzy metric spaces. We improve and generalize the well-known fixed point theorems of Banach [4] and Edelstein [8] in intuitionistic fuzzy metric spaces. Our main results are intuitionistic fuzzy version of Fang's results [10]. Further, we obtain some applications to validate our main results to product spaces.

• 대한수학회논문집
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• 제23권1호
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• pp.111-124
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• 2008

In this paper, we give some fixed point theorems on fuzzy metric spaces with an implicit relation. Our results extend and generalize some fixed point theorems on complete fuzzy metric spaces by using a new technique.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제11권2호
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• pp.108-112
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• 2011

Kaneko et a1.[4] etc many authors extended with multi-valued maps for the notion of compatible maps in complete metric space. Recently, O'Regan et a1.[5] presented fixed point and homotopy results for compatible single-valued maps on complete metric spaces. In this paper, we will establish some common fixed point theorems using compatible maps in intuitionistic fuzzy metric space.

• Korean Journal of Mathematics
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• 제29권3호
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• pp.455-466
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• 2021

Coupled fixed point results have attracted much attention among the researchers in recent times specially in the field of fuzzy metric spaces. In this paper we established a coupled fixed point result for weakly compatible mappings in G-fuzzy metric spaces. We have deduced a corollary to our main theorem. Our result also supported by examples.

• Korean Journal of Mathematics
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• 제28권4호
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• pp.915-929
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• 2020

We prove a fixed point theorem for generalized asymptotic pointwise nonexpansive mapping in the setting of a hyperbolic space. A one-step iterative scheme approximating common fixed point of two generalized asymptotic pointwise (quasi-) nonexpansive mappings in this setting is provided. We obtain ∆-convergence and strong convergence theorems of the iterative scheme for two generalized asymptotic pointwise nonexpansive mappings in the same setting. Our results generalize and extend some related results in the literature.

• Kyungpook Mathematical Journal
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• 제61권2호
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• pp.441-453
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• 2021

In this work, we define the concept of a mixed G-monotone mapping on a modular metric space endowed with a graph, and prove some fixed point theorems for this new class of mappings. Results of this paper extend coupled fixed point theorems from partially ordered metric spaces into the modular metric spaces endowed with a graph. An example is presented to illustrate the new result.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.685-700
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• 2021

In this paper, we discuss the existence and uniqueness of fixed point and common fixed point theorems in complex valued extended b-metric spaces for a pair of mappings satisfying some rational contraction conditions which generalized and unify some well-known results in the literature.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.949-959
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• 2021

In this paper, some fixed point theorems for new type of (𝜉, 𝛽)-expansive mappings of type (S) and type (T) using control function and 𝛽-admissible function in 𝒢-metric spaces are proved. Further, we prove certain fixed point results by relaxing the continuity condition.