• 대한수학회논문집
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• 제25권4호
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• pp.583-607
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• 2010

The purpose of this paper is to prove strong convergence theorems for common fixed points of two families of weak relatively nonexpansive mappings and a family of equilibrium problems by a new monotone hybrid method in Banach spaces. Because the hybrid method presented in this paper is monotone, so that the method of the proof is different from the original one. We shall give an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping in Banach space $l^2$. Our results improve and extend the corresponding results announced in [W. Takahashi and K. Zembayashi, Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings, Fixed Point Theory Appl. (2008), Article ID 528476, 11 pages; doi:10.1155/2008/528476] and [Y. Su, Z. Wang, and H. Xu, Strong convergence theorems for a common fixed point of two hemi-relatively nonexpansive mappings, Nonlinear Anal. 71 (2009), no. 11, 5616?5628] and some other papers.

• 대한수학회보
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• 제45권3호
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• pp.467-475
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• 2008

The aim of the present paper is three fold. Firstly, we obtain common fixed point theorems for a pair of selfmaps satisfying nonexpansive or Lipschitz type condition by using the notion of pointwise R-weak commutativity but without assuming the completeness of the space or continuity of the mappings involved (Theorem 1, Theorem 2 and Theorem 3). Secondly, we generalize the results obtained in first three theorems for four mappings by replacing the condition of noncompatibility of maps with the property (E.A) and using the R-weak commutativity of type $(A_g)$ (Theorem 4). Thirdly, in Theorem 5, we show that if the aspect of noncompatibility is taken in place of the property (E.A), the maps become discontinuous at their common fixed point. We, thus, provide one more answer to the problem posed by Rhoades [11] regarding the existence of contractive definition which is strong enough to generate fixed point but does not forces the maps to become continuous.

• East Asian mathematical journal
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• 제27권5호
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• pp.565-572
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• 2011

In this paper we prove common fixed point of weakly compatible maps without continuity in Menger spaces. We show that continuity of any mapping is not required for the existence of fixed point. We improve some earlier results.

• 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.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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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.

• East Asian mathematical journal
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• 제23권1호
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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].

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제12권1호
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• pp.17-31
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• 2005

In this paper we prove common fixed point theorems for three mappings under the condition of weak compatible mappings, without taking any function continuous in fuzzy metric space and then extend this result to fuzzy 2-metric space and fuzzy 3-metric space.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제12권4호
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• pp.289-306
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• 2005

The aim of this paper is to prove some common fixed point theorems for six discontinuous mappings in non complete fussy metric spaces with condition of weak compatibility.

• 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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• 제18권3호
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• pp.201-217
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• 2011

The aim of this paper is to define a new commutativity condition for a pair of self mappings i.e., (DS)-weak commutativity condition, which is weaker that compatibility of mappings in the settings of intuitionistic Menger spaces. We show that a common fixed point theorem can be proved for nonlinear contractive condition in intuitionistic Menger spaces without assuming continuity of any mapping. To prove the result we use (DS)-weak commutativity condition for mappings. We also give examples to validate our results.