• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.1027-1034
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• 2015

As a natural generalization of the contact metric manifolds, Kim, Park and Sekigawa discussed quasi contact metric manifolds based on the geometry of the corresponding quasi $K{\ddot{a}}hler$ cones. In this paper, we show that a quasi contact metric manifold is a contact manifold.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1299-1306
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• 2020

An almost contact metric manifold is called a quasi contact metric manifold if the corresponding almost Hermitian cone is a quasi Kähler manifold, which was introduced by Y. Tashiro [9] as a contact O*-manifold. In this paper, we show that a quasi contact metric manifold with Killing characteristic vector field is a K-contact manifold. This provides an extension of the definition of K-contact manifold.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.485-495
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• 2022

The aim of this paper is to characterize K-contact and Sasakian manifolds whose metrics are generalized quasi-Einstein metric. It is proven that if the metric of a K-contact manifold is generalized quasi-Einstein metric, then the manifold is of constant scalar curvature and in the case of a Sasakian manifold the metric becomes Einstein under certain restriction on the potential function. Several corollaries have been provided. Finally, we consider Sasakian 3-manifold whose metric is generalized quasi-Einstein metric.

• The Pure and Applied Mathematics
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• v.30 no.4
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• pp.407-416
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• 2023

In this paper, we introduce the concept of C^*-algebra-valued quasi b-metric space and prove some existence and uniqueness theorems. Furthermore, we prove the Hyers-Ulam stability results for fixed point problems via C^*-algebra-valued extended quasi b-metric space.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.819-830
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• 2019

This paper is mainly concerned with the existence and uniqueness of fixed points of $f:X^k{\rightarrow}X$, $k{\in}{\mathbb{N}}$, where X is a quasi-partial metric space and mapping f satisfies appropriate conditions. Results are also supported with relevant examples.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.967-970
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• 2018

The aim of this paper is to show that there exists a weakly quasisymmetric homeomorphism $f:(X,d){\rightarrow}(Y,d^{\prime})$ between two locally compact non-complete metric spaces such that $f:(X,d_h){\rightarrow}(Y,d^{\prime}_h)$ is not quasi-isometric, where dh denotes the Gromov hyperbolic metric with respect to the metric d introduced by Ibragimov in 2011. This result shows that the answer to the related question asked by Ibragimov in 2013 is negative.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.1027-1035
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• 2011

In this paper, we introduce the concept of generalized weak q-contractivity for multivalued maps defined on quasi-metric spaces. A new fixed point theorem for these maps is established. The convergene of iterate schem of the form $x_n+1\;{\in}\;Fx_n$ is investigated. And a new periodic point theorem for weakly q-contractive self maps of quasi-metric spaces is proved.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.903-920
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• 2022

In this paper, we propose and study an implicit iteration process for a finite family of total asymptotically quasi-nonexpansive mappings and a finite family of asymptotically quasi-nonexpansive mappings in the intermediate sense in convex metric spaces and establish some strong convergence results. Also, we give some applications of our result in the setting of convex metric spaces. The results of this paper are generalizations, extensions and improvements of several corresponding results.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.599-608
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• 2010

In this paper, we introduce the concept of generalized weak contractivity for set-valued maps defined on quasi metric spaces. We analyze the existence of fixed points for generalized weakly contractive set-valued maps. And we have Nadler's fixed point theorem and Banach's fixed point theorem in quasi metric spaces. We investigate the convergene of iterate schem of the form $x_{n+1}{\in}Fx_n$ with error estimates.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.251-263
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• 2023

In the setting of extended quasi b-metric spaces, we introduce a new concept called "extended A-contraction". We then use our concept to prove a common fixed point result for a pair of self mappings under a set of conditions. Also, we provide the concepts of extended B-contraction and extended R-contraction. We then establish a common fixed point under these new contractions. Our results generalize many existing result of fixed point in metric spaces. Furthermore, we give an example to illustrate and support our result.