• 대한수학회지
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• 제53권5호
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• pp.1037-1056
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• 2016

In this paper, we define the concepts of commute proximally, dominate proximally, weakly dominate proximally, proximal generalized ${\varphi}$-contraction and common best proximity point in probabilistic Menger space. We prove some common best proximity point and common fixed point theorems for dominate proximally and weakly dominate proximally mappings in probabilistic Menger space under certain conditions. Finally we show that proximal generalized ${\varphi}$-contractions have best proximity point in probabilistic Menger space. Our results generalize many known results in metric space.

• 대한수학회논문집
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• 제24권4호
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• pp.529-537
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• 2009

Generalized Menger space introduced by the present authors is a generalization of Menger space as well as a probabilistic generalization of generalized metric space introduced by Branciari [Publ. Math. Debrecen 57 (2000), no. 1-2, 31-37]. In this paper we prove a Kannan type fixed point theorem in generalized Menger spaces. We also support our result by an example.

• 충청수학회지
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• 제17권1호
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• pp.1-17
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• 2004

In this paper, the concept of semi-compatibility in Menger space is introduced and it is used to prove results on the existence of a unique common fixed point of four self-maps. These results are a very wide improvement of Mishra [8], Dedeic and Sarapa [3, 4], Cain and Kasril [1], and Sehgal and Bharucha Reid [10].

• East Asian mathematical journal
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• 제21권1호
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• pp.65-76
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• 2005

In this paper the concept of semi-compatibility has been introduced in Menger space and it has been applied to prove results on existence of unique common fixed point of four self maps satisfying an implicit relation. It results in a generalization of Banach contraction principle established by Sehgal and Bharucha-Reid in [8] All the result presented in this paper are new.

• East Asian mathematical journal
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• 제24권4호
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• pp.359-368
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• 2008

The object of this paper is to establish a unique common fixed point theorem through weak compatibility for a sequence of self-maps satisfying a generalized contractive condition in a generalized Menger space. It improves and generalizes the result of Milovanovic-Arandelovic [2], Vasuki [10] and Sehgal and Bharucha-Reid [8]. All the results presented in this paper are new.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권3호
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• pp.181-198
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• 2013

C. Vetro [4] gave the concept of weak non-Archimedean in fuzzy metric space. Using the same concept for Menger PM spaces, Mishra et al. [22] proved the common fixed point theorem for six maps, Also they introduced semi-compatibility. In this paper, we generalized the theorem [22] for family of maps and proved the common fixed point theorems using the pair of semi-compatible and reciprocally continuous maps for one pair and R-weakly commuting maps for another pair in Menger WNAPM-spaces. Our results extends and generalizes several known results in metric spaces, probabilistic metric spaces and the similar spaces.

• 대한수학회보
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• 제37권3호
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• pp.569-575
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• 2000

In this paper, a unique common fixed point theorem for a sequence of mutually contractive and commuting sequence of self mappings on Menger spaces has been proved.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제10권4호
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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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• 제30권5_6호
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• pp.729-740
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• 2012

In this paper, we prove common fixed point theorems for occasionally weakly compatible maps in Menger spaces with a continuous t-norm of H-type. As application to our results, we obtain the corresponding fixed point theorems in metric spaces. Our results improve and generalize many known results in Menger spaces as well as in metric spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권2호
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• pp.135-151
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• 2008

The purpose of this paper is to prove some common fixed point theorems for finite number of discontinuous, noncompatible mappings on non complete Menger spaces. Our results extend, improve and generalize several known results in Menger spaces. We give formulas for total number of commutativity conditions for finite number of mappings.