• East Asian mathematical journal
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• v.23 no.1
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• pp.123-133
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• 2007

In this paper we prove common fixed point theorem for four mappings, under the condition of compatible mappings of type ($\alpha$) in Menger space, without taking any function continuous. We improve results of Pathak, Kang and Baek [13] and Cho, Murthy and Stojakovic [37].

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.627-640
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• 2000

In this paper, we shall prove a fixed point theorem which is more general than that of Ciric, Kannan and Rhoades.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.425-434
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• 2007

We iteratively generate a sequence of measurable mappings and study necessary conditions for its convergence to a random fixed point of random nonexpansive operator. A random fixed point theorem for random nonexpansive operator, relaxing the convexity condition on the underlying space, is also proved. As an application, we obtained random fixed point theorems for Caristi type random operators.

• 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].

• 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].

• The Pure and Applied Mathematics
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• v.20 no.3
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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.

• Kyungpook Mathematical Journal
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• v.28 no.1
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• pp.97-106
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• 1988

In the first section of this paper two common fixed point results for four nonlinear mappings which are pairwise commuting and only two of them being continuous have been given on a complete metric space and on a compact metric space respectively which generalize the results of Mukherjee [2] and Yeh [4]. Further two common fixed point theorems have been established for two finite families of non linear mappings, with only one family being continuous. In another section we extend Theorem 3 and Theorem 4 of Mukherjee [2] for common fixed point of four continuous mappings on a Hausdorff space and on a compact metric space respectively. In the same spaces, these two results have been further generalized for two finite families of continuous mappings.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.273-288
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• 2021

We proposed to give some new 𝜓-coupled fixed point theorems using simulation function coupled with other control functions in a complete partially ordered metric space which includes many related results. Further we prove the existence of solution of a fractional integral equation by using this fixed point theorem and explain it with the help of an example.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.13-33
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• 2021

The aim of this paper is to establish common fixed point theorems under generalized (ψ - ϕ)-weak contractions in the setting of complete S-metric spaces and we support our result by some examples. Also an application of our results, we obtain some fixed point theorems of integral type. Our results extend Theorem 2.1 and 2.2 of Doric [5], Theorem 2.1 of Dutta and Choudhury [6], and many other several results from the existing literature.

• Bulletin of the Korean Mathematical Society
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• v.36 no.3
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• pp.533-541
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• 1999

In this paper, we will study controllability of some case s an initial condition $\phi$ included in some approximated phase space. To this prove we used to the Schauder fixed point theorem.