• The Pure and Applied Mathematics
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• v.28 no.1
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• pp.1-13
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• 2021

In this note we use a generalization of coincidence point(a property which was defined by [1] in symmetric spaces) to prove common fixed point theorem on S-metric spaces for weakly compatible maps. Also the results are used to achieve the solution of an integral equation and the bounded solution of a functional equation in dynamic programming.

• The Pure and Applied Mathematics
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• v.10 no.4
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• pp.245-254
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• 2003

In this paper we prove common fixed point theorems for four mappings, under the condition of weakly compatible mappings in Menger spaces, without taking any function continuous. We improve results of [A common fixed point theorem for three mappings on Menger spaces. Math. Japan. 34 (1989), no. 6, 919-923], [On common fixed point theorems of compatible mappings in Menger spaces. Demonstratio Math. 31 (1998), no. 3, 537-546].

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.1067-1075
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• 2012

In this paper we generalize the results of Ili$\acute{c}$ and Rako$\check{c}$evi$\acute{c}$. Also, we generalize one of Berinde's results to cone metric spaces. And we introduce the notion of compatible mappings of type (BC), and we establish a common fixed point theorem for these mappings.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.891-908
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• 1996

Let (X,d) be a metric space and let T be a mapping from X into itself. We say that a metric space (X,d) is T-orbitally complete if every Cauchy sequence of the form ${T^{n_i}x}_{i \in N}$ for $x \in X$ converges to a point in X.

• East Asian mathematical journal
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• v.22 no.1
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• pp.35-51
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• 2006

This paper deals with a general contraction. Two fixed-point theorems for a limit weak-compatible pair of a multi-valued map and a self map on a D-metric space have been established. These results improve significantly, the main results of Dhage, Jennifer and Kang [5] by reducing its assumption and generalizing its contraction simultaneously. At the same time some results of Singh, Jain and Jain [12] are generalized from a self map to a pair of a set-valued and a self map. Theorems of Veerapandi and Rao [16] get generalized and improved by these results. All the results of this paper are new.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.241-248
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• 2006

We define a G-fuzzy congruence, which is a generalized fuzzy congruence, and characterize the G-fuzzy congruence generated by a left and right compatible fuzzy relation on a semigroup.

• Korean Journal Plant Pathology
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• v.10 no.2
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• pp.83-91
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• 1994

Stem tissues of tomato plants (cv. Kwanyang) inoculated with Phytophthora capsici were examined by light and electron microscopy to compare early cytological differences between comaptible and incompatible interactions of tomatoes with the fungus. Twenty four hours after inoculation, the compatible isolate S 197 colonized severely the epidermis, cortex, and xylem vessels of stem tissue, whereas only few fungal cells colonized the stem tissues inoculated with the incompatible isolate CBS 178.26. Fragmented plasma membrane, distorted chloroplast, degraded cell wall, remnants of host cytoplasm were early ultrastructural features of the damaged host cell observed both in the compatible and incompatible interaction, a number of vesicles were distributed in the space between fungal cell walls and plasma membrane. The degradation of host cell walls by P. capsici was more pronounced in the compatible than the incompatible interactions. The incompatible interactions of tomato cells with P. capsici were characterized by formation of host cell wall apposition in the cortical parenchyma cells, indicating that the apposition of electron-dense material from the host cell walls may function as a plant defense reaction to the fungus. The fungal cells encased by wall appositions had abnormal cytoplasm and separated plasma membranes. The haustorium which formed from the fungal hyphae did not further penetrate through the host wall apposition and cytoplasmic aggregation, especially in the incompatible reactions. In contrast, the haustorium of the compatible isolate S 197 was not encased by wall appositions.

• Honam Mathematical Journal
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• v.39 no.1
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• pp.115-126
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• 2017

In this paper, we aim to prove certain common fixed point theorems for a pair of weakly compatible mappings satisfying (CLRg) (or (E.A)) property in the bicomplex valued metric spaces. We also provide some examples which support the main results here.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.199-215
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• 2014

Owing to the development of the notion of normal adjacency of a digital product [9], product properties of digital topological properties were studied efficiently. To equivalently represent a normal adjacency of a digital product, the present paper proposes an S-compatible adjacency of a digital product. This approach can be helpful to understand a normal adjacency of a digital product. Finally, using an S-compatible adjacency of a digital product, we can study product properties of digital topological properties, which improves the presentations of the normal adjacency of a digital product in [9] and [5, 6].

• Biotechnology and Bioprocess Engineering:BBE
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• v.5 no.1
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• pp.32-39
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• 2000

Simultaneous isomerisation and fermentation (SIF) of xylose and simultaneous isomerisation and cofermentation (SICF) of glucose-xylose mixture was carried out by the yeast Saccharomyces cerevisiae in the presence of a compatible xylose isomerase. The enzyme converted xylose to xylulose and S. cerevisiae fermented xylulose, along with glucose, to ethanol at pH 5.0 and $30^{\circ}C$. This compatible xylose isomerase from Candida boidinii, having an optimum pH and temperature range of 4.5-5.0 and $30-35^{\circ}C$ respectively, was partially purified and immobilized on an inexpensive, inert and easily available support, hen egg shell. An immobilized xylose isomerase loading of 4.5 IU/(g initial xylose) was optimum for SIF of xylose as well as SICF of glucose-xylose mixture to ethanol by S. cerevisiae. The SICF of 30 g/L glucose and 70 g xylose/L gave an ethanol concentration of 22.3 g/L with yield of 0.36 g/(g sugar consumed) and xylose conversion efficiency of $42.8\%$.