• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.1105-1114
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• 2021

In this paper, we prove a fixed point theorem for G-contractive type non-self mapping in cone metric space endowed with a graph. Our result generalizes many results in the literature and provide a new pavement for solving nonlinear functional equations.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.1053-1071
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• 2022

The purpose of this article is to establish some fixed point theorems, a common fixed point theorem and a coincidence point theorem via contractive type condition in the framework of complete partial metric spaces and give some examples in support of our results. As an application to the results, we give some fixed point theorems for integral type contractive conditions. The results presented in this paper extend and generalize several results from the existing literature.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.993-1005
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• 2013

In this paper, to include more generalized cases, the authors present a modified concept for the tripled and quadruple fixed point of the mixed monotone mappings. Also, they investigate the existence and uniqueness of fixed point of the ordered monotone operator with the Matkowski contractive conditions in the partial ordered metric spaces. As the direct consequences, the existence of coupled fixed point, tripled fixed point and quadruple fixed point are explored at the common framework and some previous results in [T. G. Bhaskar and V. Lakshmikan-tham, Fixed point theory in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379-1393; V. Berinde and M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011), no. 15, 4889-4897; E. Karapinar and N. V. Luong, Quadruple fixed point theorems for nonlinear contractions, Computers and Mathematics with Applications (2012), doi:10.1016/j.camwa.2012.02061] are improved. Finally, some fixed point theorems are proved.

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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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.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.559-580
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• 2024

In this paper, we aim to prove coupled and common coupled fixed point theorems for contractive type conditions in the context of partial metric spaces by means of a control function, and to provide some corollaries of the established results. This paper presents a number of results that generalize and extend previous work in the field. In order to better illustrate the process, we provide examples.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.247-257
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• 1997

It was the turning point in the "fixed point arena" when the notion of weak commutativity was introduced by Sessa [9] as a sharper tool to obtain common fixed points of mappings. As a result, all the results on fixed point theorems for commuting mappings were easily transformed in the setting of the new notion of weak commutativity of mappings. It gives a new impetus to the studying of common fixed points of mappings satisfying some contractive type conditions and a number of interesting results have been found by various authors. A bulk of results were produced and it was the centre of vigorous research activity in "Fixed Point Theory and its Application in various other Branches of Mathematical Sciences" in last two decades. A major break through was done by Jungck [3] when he proclaimed the new notion what he called "compatibility" of mapping and its usefulness for obtaining common fixed points of mappings was shown by him. There-after a flood of common fixed point theorems was produced by various researchers by using the improved notion of compatibility of mappings. of compatibility of mappings.