Common fixed point theorems for families of weakly compatible maps

irić, Ljubomir; Razani, ‪Abdolrahman; Radenović, Stojan; Ume, Jeong Sheok

doi:10.1016/j.camwa.2007.10.009

Cited by 15 publications

(8 citation statements)

References 14 publications

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“…(2) Theorem 37 improves and extends the result ofĆirić et al [5] and Pathak et al [25]. Now, we indicate that Theorem 37 can be utilized to derive common fixed point theorems for any finite number of mappings.…”

Section: Corollary 36 Let and Be Self-mappings Of A Metric Space ( supporting

confidence: 68%

“…By a routine calculation, one can verify inequality (49) with = 1/2. Also, ( ) = {5, 15} ⊂ [5,17] = ( ) and ( ) = {5, 10} ⊂ [5,11] …”

Section: Remark 28 In General the Converse Of Lemma 27 Is Not True mentioning

confidence: 99%

“…Hence, one is always required to improve one or more of these conditions to prove a new fixed point theorem. In the recent past, several authors have contributed to the vigorous development of metric fixed point theory (e.g., [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]). …”

Section: Introductionmentioning

confidence: 99%

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Employing Common Limit Range Property to Prove Unified Metrical Common Fixed Point Theorems

Imdad

Chauhan²

2013

International Journal of Analysis

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The purpose of this paper is to emphasize the role of "common limit range property" to ascertain the existence of common fixed point in metric spaces satisfying an implicit function essentially due to the paper of . As an application to our main result, we derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results including the ones contained in the paper of . We also furnish some illustrative examples to support our main results.

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Section: Corollary 36 Let and Be Self-mappings Of A Metric Space ( supporting

confidence: 68%

“…By a routine calculation, one can verify inequality (49) with = 1/2. Also, ( ) = {5, 15} ⊂ [5,17] = ( ) and ( ) = {5, 10} ⊂ [5,11] …”

Section: Remark 28 In General the Converse Of Lemma 27 Is Not True mentioning

confidence: 99%

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Employing Common Limit Range Property to Prove Unified Metrical Common Fixed Point Theorems

Imdad

Chauhan²

2013

International Journal of Analysis

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“…The measurements data φ are synthetic, that is, generated by a numerical computation: we fix a support source ω * , solve the diffusion problem (3) and extract the measurement φ by computing ψ on Γ. To make the numerical simulations presented here, we use P 2 finite elements discretization to solve the problems (16), (17), (9) and (10).…”

Section: Numerical Resultsmentioning

confidence: 99%

“…where θ N [0] and θ D [0] solve respectively problems (16) and 17with f = 0. Our reconstruction procedure is a non-iterative algorithm based on the following steps.…”

Section: Numerical Resultsmentioning

confidence: 99%

A non-iterative reconstruction method for bioluminescence tomography

Hrizi

2020

Filomat

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In this paper, we study an inverse source problem of the bioluminescence tomography in three dimensional case. Our aim is to reconstruct a bioluminescent source distribution within a body from the knowledge of the boundary measurements. The inverse source problem is reformulated as a topology optimization one minimizing an energy like type functional. It measures the difference between the solutions of two auxiliary boundary value problems. An asymptotic expansion of the considered functional with respect to a set of ball-shaped anomalies is computed using the topological sensitivity analysis method. The obtained theoretical result leads to build a non-iterative reconstruction algorithm. Finally, some numerical examples in 3D are presented in order to show the effectiveness of the devised reconstruction algorithm.

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