• East Asian mathematical journal
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• v.21 no.1
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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.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.743-752
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• 2011

Fixed point theorems for two hybrid pairs of single valued and multivalued noncompatible maps under strict contractive condition are proved, without appeal to continuity of any map involved therein and completeness of underlying space. These results extend, unify and improve the earlier comparable known results.

• 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.

• East Asian mathematical journal
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• v.32 no.5
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• pp.701-716
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• 2016

We establish a tripled coincidence and common tripled fixed point theorem for hybrid pair of mappings satisfying new contractive condition. To find tripled coincidence points, we do not use the continuity of any mapping involved therein. An example is also given to validate our result. We improve, extend and generalize several known results.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.373-382
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• 2015

In this paper, we introduce and study a new multivalued mapping in $\mathbb{R}$-trees, called k-strictly pseudononspreading. We also introduce a new two-step iterative process for two k-strictly pseudononspreading multivalued mappings in $\mathbb{R}$-trees. Strong convergence theorems of the proposed iteration to a common fixed point of two k-strictly pseudononspreading multivalued mappings in $\mathbb{R}$-trees are established. Our results improve and extend the corresponding results existing in the literature.

• East Asian mathematical journal
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• v.27 no.5
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• pp.527-538
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• 2011

In this paper, we introduce a new iterative scheme for finding a common element of the set of an equilibrium problem, the set of fixed points of nonexpansive mapping and the set of solutions of the generalized variational inequality for ${\alpha}$-inverse strongly g-monotone mapping in a Hilbert space. Under suitable conditions, strong convergence theorems for approximating a common element of the above three sets are obtained.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.257-267
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• 2021

In this paper, we develop an iterative algorithm for obtaining common solutions to the Cayley inclusion problem and the set of fixed points of a non-expansive mapping in Hilbert spaces. A numerical example is given for the justification of our claim.

• The Pure and Applied Mathematics
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• v.28 no.2
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• pp.103-110
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• 2021

The aim of this paper is to prove a common fixed point theorem for two w-compatible maps in modular A-metric spaces. The main result is also illustrated by an example to demonstrate the degree of validity of our hypothesis.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.163-176
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• 2022

In this paper, we introduce some new classes of generalized mappings and prove some common fixed point theorems for a pair of asymptotically regular mappings. Our results extend and improve various well-known results due to Kannan, Reich, Wong, Hardy and Rogers, Ćirić, Jungck, Górnicki and many others. In addition to it, a sequential fixed point for a mapping which is the point-wise limit of a sequence of functions satisfying Ćirić-Proinov-Górnicki type mapping has been proved. Supporting examples have been given in strengthening hypotheses of our established theorems.

• East Asian mathematical journal
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• v.27 no.1
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• pp.35-49
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• 2011

In this paper, we study multi-step iterative algorithm with errors and give the necessary and sufficient condition to converge to com mon fixed points for a finite family of asymptotically quasi-nonexpansive type mappings in Banach spaces. Also we have proved a strong convergence theorem to converge to common fixed points for a finite family said mappings on a nonempty compact convex subset of a uniformly convex Banach spaces. Our results extend and improve the corresponding results of [2, 4, 7, 8, 9, 10, 12, 15, 20].