• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.565-580
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• 2021

In this paper, first of all we prove a fixed point theorem for 𝜓_∫𝜑-weakly contractive mapping. Next, we prove some common fixed point theorems for a pair of weakly compatible self maps along with E.A. property and (CLR) property. An example is also given to support our results.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.601-610
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• 2021

A convergence theorem for a generalized 𝜑-weakly contractive mapping is proved which satisfy a generalized contraction condition on a complete metrically convex metric space. The result in this paper generalizes the relevant results due to Rhoades [18], Alber and Guerre-Delabriere [1], Khan and Imdad [14], Xue [20] and others. An illustrative example is also furnished in support of our main result.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1151-1164
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• 2009

Let E be a reflexive Banach space with a weakly sequentially continuous duality mapping, C be a nonempty closed convex subset of E, f : C $\rightarrow$C a contractive mapping (or a weakly contractive mapping), and T : C $\rightarrow$ C a nonexpansive mapping with the fixed point set F(T) ${\neq}{\emptyset}$. Let {$x_n$} be generated by a new composite iterative scheme: $y_n={\lambda}_nf(x_n)+(1-{\lambda}_n)Tx_n$, $x_{n+1}=(1-{\beta}_n)y_n+{\beta}_nTy_n$, ($n{\geq}0$). It is proved that {$x_n$} converges strongly to a point in F(T), which is a solution of certain variational inequality provided the sequence {$\lambda_n$} $\subset$ (0, 1) satisfies $lim_{n{\rightarrow}{\infty}}{\lambda}_n$ = 0 and $\sum_{n=0}^{\infty}{\lambda}_n={\infty}$, {$\beta_n$} $\subset$ [0, a) for some 0 < a < 1 and the sequence {$x_n$} is asymptotically regular.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.257-265
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• 2011

In this paper, we first prove a common fixed point theorem for generalized nonlinear contraction mappings in complete metric spaces there by generalizing and extending some known results. Then we present this result in the context of ordered metric spaces by using monotone non-decreasing mapping.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.1-16
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• 2013

The aim of this paper is to establish a new fixed point theorem for a set-valued mapping defined on a metric space satisfying a weak contractive type condition and to establish a new common fixed point theorem for a pair of set-valued mappings defined on a metric space satisfying a weak contractive type inequality. And we give periodic point theorems for single-valued mappings defined on a metric space satisfying weak contractive type conditions.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.607-614
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• 2008

We present coincidence points and common fixed point results for (f, g)-contractive mapping and (f, g)-nonexpansive mappings. Our results generalize and complement various known results existing in the literature.

• 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.

• Honam Mathematical Journal
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• v.45 no.1
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• pp.1-24
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• 2023

In the present paper, we prove common fixed point theorems for a pair of weakly compatible mappings under implicit contractive relation in quasi-partial S_b-metric spaces. We also provide an illustrative example to support our results. Furthermore, we will use the results obtained for application to two boundary value problems for the second-order differential equation. Also, we prove a common solution for the nonlinear fractional differential equation.

• The Pure and Applied Mathematics
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• v.21 no.3
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• pp.165-181
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• 2014

We establish a common n-tupled fixed point theorem for hybrid pair of mappings under new contractive condition. It is to be noted that to find n-tupled coincidence point, we do not use the condition of continuity of any mapping involved. An example supporting to our result has also been cited. We improve, extend and generalize several known results.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.305-323
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• 2021

In the present paper, utilizing (𝜙, 𝜓)-weak contractive conditions, unique fixed point and some coincidence point results have been studied in the context of cone 2- metric spaces. Also, our obtained results generalize some results from cone metric space to cone 2-metric space. For the authenticity of the presented work, a non trivial example is also provided.